To the OP;
Your best bet is to get advice from people in your area that spend a lot of time in the woods and/or actually hunt black bears and mountain lions in the area you plan to spend time in. These are the people that would have first-hand knowledge about the animals in question and what they prefer to use when they come into violent contact with them.
That said, in general, you want to carry something that will over-penetrate a bear or a cat; you don't necessarily care that much about bullet expansion with an aggressive large predator. The reason being that these animals are large enough that it will take some time for any of them to bleed out; what is required is either a CNS hit or a debilitating hit, i.e., shattering a hip/shoulder blade, leg bone so as to drop the animal or at least slow their advance significantly.
These aren't my sentiments, btw. Many years ago I spent a month fishing the back country in both WY and MT, where I knew I could possibly run into a griz, so I asked the people that I knew that had some experience encountering these animals in the wild. I have a couple friends, from AK that are both bear hunting guides; we went to flight school together back in the day. These guys between them and their fathers (also AK hunting guides) have more than a century of experience hunting and being near big bears, so I figured they would know what they were talking about.
Their first answer was an 18 inch barreled 12 ga. shotgun loaded with hard cast slugs. They were unanimous in that respect. I told them I didn't want to carry a shotgun while fly-fishing, and they both told me at minimum I should carry a .44 mag, again using hard cast slugs. Now, both of them told me various stories of people that had killed grizzlies with calibers less than a .44 mag, but they both felt that these cases were out-liers, and that I should carry more than enough gun, provided I could quickly and accurately shoot the thing. If I could not, they advised at least .357s or a 10 mm, again using loads as hot as I could handle.
As for black bears, both advised me that a .44 mag probably wasn't necessary, and that either .357 mag or 10 mm would be adequate to the task.
They also told me that bear spray was probably a good idea, since most people don't shoot well with 300+ lbs. of angry bear sprinting towards them, and if you can get the bear to run off because you took a little initiative and sprayed them before they got into full charge mode, they probably would take off. If they ambush you, well that's what the gun is for.
Again, these are not my opinions, as I have no actual experience hunting bears and my only confrontations with bears ended peacefully. These are the opinions of two experienced bear hunting guides, both of whom have faced charging bears more than once.
On a side note, one of my aforementioned buddies, while guiding some fly-fishermen, stood off a young griz with a fly rod on the Kenai. He estimated the bear to be about 300 lbs.
As he tells it, he was guiding three clients and this bear had just been chased out of a fishing hole below them by a larger bear. The bear decided to chase them out of their hole. It charged into their hole with my buddy armed with nothing more than a 9 ft. fly rod (they were fishing in a 'no firearms' area). He kept yelling at it while swinging the rod - actually hitting the bear in the face a few times. He yelled, "they're are four of us!" over and over, as a bear on the Kenai had never attacked a group of people larger than three. He said that his mind noted that bears probably couldn't count, but he kept yelling it anyway. Apparently, the bear finally realized that there were indeed four humans and backed down and ran off.
It's a funny campfire story; at least if you're not one of those that was there that day.
P.S. Whoops, forgot to answer the other part of your question . . . if it were me, I'd choose the .40, instead of the .45 acp, hot loaded.