It's a good question, and primarily one of range, as a tradeoff against noise.
First, range. For squirrel & rabbits, either one will be deadly on such small critters at any range at which you could make a hit under field conditions, so power / retained energy is a wash (non-issue). But, if you're not planning on practicing your holdover, then you have to look at your likely ranges. If we're talking close-in & wooded, that favors the 17 mach 2, which will shoot flat to around 125 yards. But if wide open, then the HMR gets you pretty flat shooting out to about 175 yards.
As for how MUCH quieter is mach 2 over the hmr, I dunno because I don't have a mach 2, but if it's significant at all, that's what I'd run with if the neighbors are your major concern. Surely it will be appreciably quieter I would think. Accuracy will be a wash. FWIW, I like the .17 hmr, but where I shoot, noise is not an issue.