I have all three:
IMHO, Kaufman and Peterson are roughly equivalent as far as value goes. Both are pretty up to date (although Peterson may slightly edge out Kaufman).
Petersen is the most comprehensive guide available, and has excellent illustrations, but the separation of plates and text make the guide annoying as hell to use (and really, for most mammals, range information and habitat preference is key, so having to flip back and forth is a pain in the ass)
Kaufman is smaller and easy to carry, and range maps, photos, and text are all on one page. This is usually my field guide of choice. Some of the pictures however may be less useful for some mammal groups, especially small rodents, shrews, etc. And the Peterson generally has more descriptive text, which can come in handy for tough ideas.
I actually loath the Princeton guide with every shred of my being. It has a similar format to Kaufman, but uses illustrations, not edited photos. However some of the illustrations are completely abysmal. The woodrats, rabbits, and shrews all are drawn strangely, and have a vaguely "overly muscular" look about them. Others just look off in weird ways hard to describe such as the otters plate. My edition, although not a thick or large book, was given a hardbound cover, which also makes it hard to stuff in a pocket comfortably, unless you want to risk screwing up the covers.
So yeah, I would go with Kaufman, or Peterson. If you are really hardcore into mammals and are expecting to try to see various mice or whatnot, I would probably suggest getting both. I might give the slight edge to Kaufman if I had to choose one or the other.
