I am not a lawyer and none of this should be taken as legal advice but...
Since when is the 10mm this all powerful bear stopping round? Even loaded to it's potential it doesn't exceed what the 357 magnum is capable of and most factory loads are nothing more than a warmed over 40 S&W. Anyone who thinks this is a grizzly stopper is delusional.
I understand people being concerned about overzealous prosecutors but the 10mm is, and was designed to be, a self defense cartridge. Imo, it is a very good cartridge for that purpose. For those who suggest carrying what the local LEO's carry, fine but I doubt they are carrying 357 Sigs either. Personally, having one less potential legal issue is the only reason I have any factory ammo at all, other than rimfire ammo.
Also, if you don't feel endangered enough that it becomes necessary to take someone's life in order to stop them, you shouldn't be pulling the trigger in the first place. Shooting to wound someone absolutely will leave you very vulnerable in court. It is called lethal force for a reason. Once it gets to that point, your goal should be to end the threat as quickly as possible before any harm comes to yourself or your loved ones. Someone shot in the chest with a lesser caliber will end up just as dead. The question is, will it stop them in time?
As for the original question, I think both are very good choices and I don't think you could go wrong with either one but I would personally go with the 10mm. It is hard to argue against a larger bore. I believe it is a more versatile round, easier to handload if that applies, has slightly better stopping power, and while not in the same class as a large revolver, is arguably the best of the semiauto calibers for use in the woods.