Good paper/article on the mechanisms in RBC vs New Keynesian models I have read technical books about the (baseline) RBC and New Keynesian models. 

However, these books tend not to explain very intuitively the propagation mechanisms of shocks between the two models, or the difference between them. I am referring to the mechanisms by which a shock to one variable affects the other variables. Since the baseline NK model does not contain any endogenous persistence, I'm primarily interested in how these effects play out within one time period. That is: what are all the mechanisms through which a shock propagates through the system and determines a new equilibrium $E^*$ (as opposed to the equilibrium $E$ that would have happened in that time period without the shock.)

So I'm looking for an intuitive paper/article on the internal (propagation) mechanisms in RBC and New Keynesian models. 

Note again, that I am interested in a primarily intuitive/economic explanation of these mechanisms, rather than an overly mathematical one since the latter I have already found in textbooks.
If possible, clarifying what exactly you're most interested in might help answers be more on point and useful. Are you interested in the mechanisms that cause a one-period shock to last (and not just immediately dissipate)? Or are you interested in understanding some of the reasons that a shock to one variable (say technological progress) leads to changes in other variables (output, employment, wage, interest rates, etc.)?

In either case, the answer depends somewhat on what flavor of the model you're considering. The reasons that shocks tend to have persistent effects in the models comes from mechanically inserting persistence (by using an AR process for shocks) and/or the interplay between stocks and flows (the most common being capital accumulation and investment).

As for sources, I personally found that lecture notes from graduate macro classes were often some of the most useful resources for understanding internal mechanisms and reasoning (Eric Simms, for example, has a wonderful series of lecture notes that include some outlines of BC facts that models try to explain (including persistence), basic RBC model notes, notes examining extensions to the RBC framework, notes on investment in RBC models, in addition to NK notes and some explaining optimal monetary policy in NK models). In addition to Simms' resources, Ordonez has created a nice, simple set that explain the derivation, which might provide some insight. Additionally, slide 15 in this set describes one example of how propogation can work, though again, that's quite a limited example.

That said, there are several classic papers (such as Resuscitating Real Business Cycles especially section 4) which are useful to keep in mind. As for how others generate persistence, you can look at habit formation in consumption (here, though there are many others, of course), variable capital utilization, or any of the other listed methods on slides 40-46.

Though again, more info on what exactly you're looking for could help me refocus a bit. I hope these at least provide a start to what you're interested in!

EDIT: Given your interest within a single period, I think the key is to keep in mind what the "engine" is behind the RBC model- ultimately, it's all about households maximizing utility. They do this by producing (through the firm side of the RBC model) and by enjoying leisure. The specific relationship between these objects leads households to respond to changes in any single value.

For example, take a technology shock (say a positive one, so now more output can be generated from the same levels of input). There are two competing forces:

The substitution effect, which leads households to "realize" that, by increasing the number of labor hours they commit to, they can get even more output (some of which can be used for consumption, since "output" in this model isn't differentiated, and can therefore be used either for consumption or investment).

The income effect, which dictates that, since leisure is a normal good (as defined by the utility function exogenously plugged in to the model), higher consumption should lead to higher leisure as well.

Generally, models are "calibrated" such that hours worked and output both rise. So this suggests that households value the additional consumption enough so they choose to work more.

In RBC models with investment, positive technology shocks also mean that capital is more productive, which means interest rates rise.

I can write a more thorough overview from my grad macro notes later in the day, but until then, I'd review this set of Simms' notes, which do a decent job explaining where everything comes from, and why variables move the way they do. Alternatively, as this source notes: "Proposed by Kydland and Prescott, the RBC theory rests on the neoclassical concept of rational expectations and constructs on the basis of expected utility maximization. Therefore, it is important to understand the central assumption in the RBC theory: individuals and firms respond to economic events optimally all
the time." Additionally pages 10 onwards might be useful in understanding where this comes from, and this set of notes also takes more time detailing where things come from, and what they mean.

Let me know if those additional resources are helpful at all!