Are means-tested or universal programs more effective at reducing the poverty rate? Advocates of means-tested programs frequently argue that they will remove inefficiences in the system by directing a larger proportion of the program's budget to people with a genuine need. By contrast, those who oppose them, and who tend to advocate for universal programs, argue that they would require the creation of bureaucracy that would eliminate any theoretical gains. Some also argue that the portion of the money that goes to wealthier people serves as an economic stimulus which increases the overall health of the economy, thus being less inefficient than it would otherwise seem.
Which of these arguments is correct? Are means-tested programs or universal programs more effective at alleviating poverty? I am aware that there are moral arguments for both perspectives as well: some say that people who make more than a certain amount (or less, for that matter) do not deserve assistance, whereas others argue that everyone deserves equal assistance. However, I am interested in the economic point of view. In addition, some people argue that any economic assistance programs have economic effects that ultimately eliminate any gains. If there is strong evidence supporting that perspective, I would be interesting in seeing it, but the question is primarily about which of the two types of programs is more effective (or less ineffective, if both are ineffective). Obviously, this is a politically heated theme, so I am ideally looking for answers based on empirical research, case studies, and to an extent modeling,
TL;DR:
There is generally not much support for universal welfare programs (as narrowly defined - see below) in the literature. However, it is for different reasons that what is mentioned in the question.
The main proposed advantage of universal programs is that they do not distort peoples incentives since you are not loosing your benefits as you are moving up an income ladder (less administrative costs is in the literature only auxiliary argument). However, at the same time this means that state has to redistribute resources even to billionaires, so such programs are more expensive. These expenses ultimately require higher taxes and taxes distort incentives as well. It turns out that on net having means tested welfare transfers produces less distortions to the economy.
The bureaucracy issue is very commonly cited in the press, because it likely captures better peoples imagination and attention as compared to more serious but less known deadweight loss caused by taxation/redistribution.  However, bureaucracy costs are usually trivial for either system. In addition, there is no support in a literature that welfare for rich has much stimulative effect for the economy.
Full Answer:
Narrowing the Scope:
First, in order to actually answer this question, we have to properly define the scope of subject matter. 'Programs that reduce poverty' is broad and vague term that could be applied to virtually any government program. However, given what is written in the question I suspect what you are most interested in are income redistribution taxes and transfers such universal basic income (UBI) vs means tested transfer as opposed to some other government schemes (e.g. compulsory state provided elementary and high-school education could be viewed as anti-poverty program but we have to narrow the scope of the question as providing overview of all government programs that can reduce poverty in one way or another would require several books and be well beyond scope of SE answer).
Bureaucracy Issue
Next let me address the bureaucracy issue as this is very common argument that non-economists use but you won't even see it mentioned in the literature much. Simply put bureaucracy costs are trivial. For example, consider the administrative spending for main US welfare programs below:

The administrative spending ranges from $9\%$ to $&gt;1\%$ of total spending for the program. Moreover, you will note that the highest administrative costs are for food stamps and housing vouchers which are in kind/conditional cash transfers that are, generally speaking,  considered by most economists relatively inefficient for various reasons relative to unconditional (but still means tested - conditionality here refers to additional restrictions on spending of the transfer) cash transfers (e.g. see Currie &amp; Gahvari, 2008; Skoufias et al., 2013; Handa et al., 2018; Mishra &amp; Kar, 2015; Gentilini 2016 or Caldés et al., 2006).
As you can see the earned income tax credit (which is still means tested) but purely cash based transfer has less than $1\%$ administrative cost. This just goes to show that in principle means tested programs are not expensive from point of view of bureaucracy. Even if we would be generous and assume that switching to universal transfer could cut $50\%$ of all administrative costs (which I think is overtly generous given that significant part of administrative costs are fixed costs) it would be penny wise but pound foolish to make argument that such trivial savings are justifiable taking into account large costs that extending transfer to anyone entails (although as will be explained further down the road a proper efficiency argument could be made on the account of distortions they create).
Stimulus Argument
I must say I did not heard the argument that transfers to the rich provides additional stimulus to the economy (I heard the one about tax cuts but not about transfers), but it does not have any basis in economics. First, from macroeconomic perspective spending is spending whether done by rich or poor. There is not much if any evidence that spending would stimulate economy more if done by rich instead of poor.
Second, richer people tend to save higher portion of their income (see explanation in this older SE answer why), this does not matter outside recession since saving becomes investment spending which increases output equivalently to consumer spending in normal times. However, during recessions economies can experience the 'paradox of thrift' - a situation where extra saving is offset by drop in output and thus won’t help the economy  (I wont go into details on this concept as it is tangential to this question, you can see further explanation in Blanchard et al Macroeconomics: A European Perspective). But even in such an event consumer spending still stimulates the economy. Consequently, if anything if the goal is to stimulate economic activity the transfers should especially target poor who have higher propensity to consume not higher income groups who tend to save more.
Economic Efficiency Issue
When economists discuss economic efficiency of redistribution schemes they mainly focus on the economic distortions that these schemes create (see Stiglitz Economics of the Public Sector). These efficiency costs are created because taxes and redistribution distort optimal behavior of people. For example, an income tax will distort peoples incentives to work, consumption tax to consume etc. At the same getting welfare benefit conditional on low income distorts peoples incentives to move up income ladder or put more hours and so on.
The reason why economists focus on these effects is that even though these are almost unknown among general public their economic costs are massive. For example, as mentioned in Jacobs (2009) on the margin it is often believed that excess burden of taxation is approximately $50\%$ (although there is some uncertainty about this value and it could be as low as $30\%$ or as high as over $100\%$ depending on exact behavioral responses (elasticities) to taxes and country we are talking about). The commonly accepted $50\%$ figure implies that for government to raise raise $1$ dollar of tax revenue it has to reduce aggregate income of an economy by $1.5$ dollars on the margin. This is purely cost of damage to the economy, the administrative costs would have to be added on top of that, but as mentioned above they are more or less trivial (e.g.  in Netherlands where I live they would be additional 6 cents on average (see Allers, 1994) and in most developed countries it should be comparable).
Now when it comes to universal redistribution schemes their big advantage is that they eliminate distortions on the receiving side. For example, with UBI you get your welfare transfer whether you work, are poor or rich and so on. So there is absolutely no reason for you to change your behavior/economic activity. However, at the same time since the benefit is extended to everyone they are more expensive, requiring increases in taxes which as mentioned above also have serious effects on distorting the economy.
When it comes to means tested redistribution schemes they create relatively large economic disincentives at the receiving end but an advantage is that only a portion of the population receives the benefit making them much cheaper. Consequently, government needs to raise much less revenue through distortionary taxation to pay for it.
Hence, a priori it is not clear which one would create less net distortions as one creates more distortions on receiving end and the another one more on the taxing end. Consequently, the main economic debate of universal redistribution schemes vs means tested schemes is about whether the economic distortions of one are larger than other, not about administrative costs that are relatively trivial at best mentioned as an auxiliary argument/issue in the literature.
Here the literature shows that means tested schemes are preferable as they cause less distortions both from theoretical and empirical perspective. For example, the state of the art optimum income taxation simulations (that includes also redistribution which is treated as a negative tax in the literature) show that it is optimal to have means tested income redistribution, even when government adopts Rawlsian social welfare preferences (i.e. the max-min criterion, which implies that government only cares about the welfare of the poorest anyone else except for the poor has zero welfare weight in government social utility function). This is despite of the fact that such means tested programs cause distortions primarily on the receiving end and thus create a 'poverty trap' - a situation where poor have less incentive to climb up the income ladder (see Diamond 1998;  Saez 2001).  The case for broader benefits is bit more stronger under utilitarian or charitable conservative/libertarian social welfare function, but I don't know of any standard social welfare function that would result in universal benefit. This can be seen on the picture below which shows simulations of optimal marginal tax rate. The tail is so high on the lower end of income distribution precisely because that represents people loosing their benefits (withdrawal of benefit is considered tax since benefit itself is a negative tax).

If you are not convinced by theoretical optimal tax simulations then when we turn to empirical evidence on the most popular universal redistribution scheme: universal basic income (UBI), the evidence shows that the measure is simply too expensive and thus inefficient (even if it reduces the above mentioned poverty trap and has some other positive effect). For overview of literature on this you can see Hoynes and Rothstein (2019) or Martinelli (2017) and sources cited therein. The literature can be summarized nicely by the following quote form Martinelli:

an affordable UBI would be inadequate, and an adequate UBI would be unaffordable.

The issue is that there are quite a lot of people in upper income brackets. For example, in 2019 in the US over $35\%$ of households earns above $100,000$ dollars per year and about $20\%$ above $150,000$ dollars per year. These are income groups where there is little to none rationale for welfare support (at least from the point of view of welfare/public economics - politically it might be useful to support such groups for political reasons), but are still very broad groups of people that would waste enormous number of resources unless the universal benefit is set so low that it will become insufficient for those at the bottom of income distribution.
Few Caveats
However, there are few caveats that need to be mentioned.

As seen in the previous chapter taxation and redistribution cannot be divorced from each other - they are two sides of the same coin. However, if you only talk about transfers you could make an argument that you can have universal transfer while you cancel it with extra taxes on higher income groups. For example, you could give everyone $1000$ dollars per month of universal income and then tax everyone else except the poor by $1000$ dollars more essentially making the universal basic income means transfer program but in more hidden way. This is really just semantics argument hinging on definition of the words in the name of program, but some economists such as Mankiw made an argument for UBI on these grounds. However, this is to the large extent a semantic issue as economically if you cancel that $1000$ by higher taxes for better of groups you create the same disincentives as if the benefit would only exist for poor. So really this is just a semantic argument without economically affecting the discussion in sections above.
As mentioned at the beginning this analysis might not extend to every single government program. Arguments for universal education or healthcare could be made on partially redistribution grounds but address additional issues of externalities or market imperfections that make their universality necessary or more efficient, but this goes beyond any purely redistribution/poverty-alleviation concerns.