Does Dogecoin or Bitcoin have a more appropriate rate of monetary inflation? The supply of new Bitcoins and Dogecoins is depicted in the graph below.

The Bitcoin inflation rate is currently higher than the Dogecoin rate, but it reduces sharply to a rate close to zero. It eventually reaches 0% in 2140, after which there will be no new Bitcoins.

There are currently 100 billion Dogecoins. The Dogecoin inflation rate is fixed at an additional 5.256 billion coins per year for every year henceforth.



Which inflation rate is more appropriate for a general-use currency intended for use for transactions of all sizes? I realise this isn't necessarily the stated aim of either currency.

Answerers should assume that the inflation rates are sacrosanct and can't be altered in years to come.
Your coins do not have 0 inflation in the long run

First, we need to set straight that you have a critical error in your supposition: The rate of creation of money is not the only determinant of the inflation rate, see here.

Even if we ignore these equilibrium effects, is any of these coins superior in its rate of money creation?

Suppose hereinafter that the actual inflation rate mirrors the money creation rate.

The optimal inflation rate is something that is not clearly understood, but most Economists agree that it is somehow related to the current state of the economy.

Hence, an inflation rate that is independent of the state of the economy cannot be that great. It basically removes the central banking authority to manipulate the inflation rate to the greater good of society - but removing this power is also an explicit goal of many advocates of these coins. 

I have answered few reasons for and again higher inflation here. These make a case for a positive inflation rate. However importantly, they make a case for positive unexpected inflation rate. If high inflation is expected, all these benefits fall down. What remains is the shoe-leather-cost of inflation, implying that the lower inflation rate, bit coin, would be weakly better.

Remember: This is based on the false supposition that the money creation rate is the only determinant of the  inflation rate.

For the optimal rate of inflation, see also


http://www.frbsf.org/economic-research/publications/economic-letter/1997/september/what-is-the-optimal-rate-of-inflation/
http://www.nber.org/papers/w16054