For the most part, there is no difference in the external ballistics between the 10 gauge and the 3 1/2" mag 12 gauge. In factory loadings both pretty much carry the same payload at the same velocity. The 10 you could handload a little more in.
The 10, however, tends to produce cleaner patterns with the slightly larger bore than the 12.
Don't expect to find any shot sizes in the 7 1/2 or 8 range that you can take down to your local trap club and blast away. You'll be handloading if you are looking for those.
Don't expect to find any shells down at your local Walmart. Most of those you find at the sporting goods store will be goose or turkey loads. For buckshot you'll likely be mail ordering. Don't know if Dead Coyote is available in 10 gauge. I'm sure it'd be a great load.
If you plan on going to Kalistan, last I heard the 10 gauge is illegal there, although the 3 1/2" 12 gauge is not. Just goes to show how ignorant the lawmakers there are.
I've got an Ithaca Mag 10, and shooting 2 1/2 oz full loads, it recoils less than my Winchester Defender 18" shooting 2 3/4" value pack loads. It's still a good recoil though, and if you mount it wrong you'll find out quick. Much like shooting a .45 ACP vs. a .40 S&W, more of a push than a punch.
As for pelt damage, it has a lot to do with how far they are when you hit 'em. The closer they are the more holes they'll get. If you are shooting them off the muzzle you'll be looking for a needle and thread, if not a sewing machine.