The only shot that is a guarantee to stop anything is a CNS hit. On some animals it takes more penetration than others to get there. The nerve centers can be buried pretty deep behind heavy muscle & bone. The bigger the bear the more muscle mass etc is between you & the CNS.
If I were primarily going to hunt AZ & were on a budget I would probably be looking into a Contender or Encore in a rifle caliber. If you hunt primarily in brushy areas than the revolver might be the better choice. 7-30 Waters or 300 Savage (I think it's a Contender chambering) or a JDJ wildcat in the Contender, 7mm-08 or 308 are great in the Encore. There are some real deals to be had on Contenders/Encores at times & calibers are cheap & easy to add. Another plus for the Contender is that since you are already loading for the .357 you could pick up a .357 Contender barrel (often they are available fairly cheap) & be ready to go. The .357 from a 14" barrel with no cylender gap gets moving a WHOLE lot faster than it does from a 6" revolver if you use the right powders. It can be a great hunting round that is cheap & pleasent to shoot. Having had Contenders & Encores I like the feel of the original Contenders (Pre G-2) a WHOLE lot better.
If you have the discipline to keep your shot distance reasonable the GP 100 will do the job on deer-elk with he right bullets & shot angles. You just can't expect the penetration on an elk with a 180 gr bullet @ 1000fps impact speed that you can expect from a 320 or 400 at 900fps.
Whether it's your 4wd pickup in the mudhole or bullet penetration in a heavy animal, momentum is your friend!!!