If your looking for a woods only semiautomatic carry pistol there's no question the 10mm is the better choice between those two calibers... Glock 20sf vs Glock 21 for example. 10mm has better penentration, faster, higher energy, hydrostatic shock and better capacity. Only cons are price... Get a .40 conversion barrel and the issue is moot. You can practice with .40 and then use 10mm for woods carry with a box or three of full power loads to familiarize yourself.
As for bullets, you can find some guys on this forum I'm sure to load you up some bear rounds or just buy from Underwood. My buddy has a load that shoots a 200 grain Hornady XTP hollow point at 1335 FPS with over 700 pounds of energy. The best .45 stuff is a few hundred fps slower with almost 200 less pounds of energy. The 10mm has far better penentration which is important when dealing with a charging pissed off bear...
Now if your trying to find a do everything gun AND a woods carry gun then a .45 ACP would be the way to go. If it's a outdoor gun which you said it is AND your stuck between those two calibers then get the 10mm...It's far superior.

Here's a thread which deals with your original question. The 10mm is by far the chosen winner in this debate. 10mm vrs .45 ACP

Also, DocGKR one of the most well known and best ballistic experts and someone who knows more about wounds and bullets/ballistics than everyone on here combined agrees that the 10mm is a far more capable round for 2 and 4 legged defense than the .45 ACP.

Your choice though. As for a good compact .45 ACP a XD compact would be a good choice. 10 or 13rd mags.