SWAG
It depends on what you mean by stopping power. I'll intuit from your post that you mean stopping a human assailant before they can hurt you. Of course, shot placement is everything, but sometimes we don't get 'em in the heart, or head. If we did, alot of people would just carry a .22, and these debates would be moot. There are alot of very smart people here giving you correct technical information about bullet physics, shot placement and the like. And they are correct. But untill the bullet hits the dirtbag, it's all a SWAG (scientific wild ass guess). lol. Also the comparison of calibers is to simplistic, as there is alot of overlap between the two calibers depending on bullet design, bullet weight, bullet velocity, etc... All this information, although correct, can be confusing. To see what happens in the real world, I look at actual shooting statistics. Very few of us have actually shot someone, and those of us who have, have probably not shot enough people for their experiences to be statistically usefull. Although shooting animals can be very illuminating, and I would trust these experiences over alot of the science, animals are a good deal tougher than people and what stops a man best may not be what stops an animal best and vice versa. A good source of actual shooting statistics can be found in the "Stopping Power" books written by Marshal and Sanow. I recommend you buy them. If the statistical sample is large enough, variables like shot placement tend to average out somewhat. I know it's not perfect, but unless we do "strassburg tests" on death row inmates, it's as close to the real thing as we are likely to get. If memory serves me, both the Federal 230gr Hydra-shok, and the Remington 185gr Golden Saber are at the top of the heap in .45 auto, at near 96%. Most 10mm's will get you more range and penetration though. I think the best performers in the 10mm catagory are the Federal 155gr jhp and the Cor-Bon 150gr jhp's at around 90%, but with the 10mm there have not been enough shootings with the respective bullet types to be statistically reliable. Also some of the more powerfull rounds from Doubletap and the like are not in the sample (probably too much kick for alot of departments to go with). In the end, either will do (no pun intended).
My personal choices (not nessesarily yours): As most actual shootings occur at very close distances, where range and penetration are not as much of an issue, my CWP gun is a .45. I load it with the Remmington 185gr Golden saber's. They are a little lighter and faster than the Hydra-shoks, and recoil is a little less so I can double tap a little faster with them. When out hunting in the field I go with the 10mm, and load them with Doubletap's 165gr Golden saber at 1425 feet per second and 744 footpounds of energy, for protection against "big bitey scratchy things". If your pistol has a conventionally rifled barrel, you might go with Doubletap's 200gr hardcast at 1300 feet per second for bear and such, but your range for hunting may suffer, and I have seen them suffer from stabilization problems effecting accuracy, but if attacked by a bear, "minute of bear" accuracy will do. I hope I was helpfull. Mick P.S. If in bear country, consider carrying a .500 S&W mag or similarly powered pistol. If I had to fight a large brown bear with a 10mm or a .45, I think I would shat in my pants. The "big bitey scratchy things" down here in florida are not that big.