Here in Wyoming, "predator" means something a bit different then it does in Florida.

My most used "Varmint Rifle" is an accurate AR15 in 5.56 NATO. It's used for killing critters up to about 60 pounds.

For Mountain Lion, Bears, (both Blacks and Grizzlys) and Wolves I'd use what every big game rifle I have in my hands at the time. In my hands is the key here.
When hunting antelope or deer in some places, any "deer rifle" is as good as any dedicated "predator" rifle. But when hunting in the areas where I see a lot of Grizzlies I have a tendency to carry bigger rifles. I have killed a lot of elk with 270s, but I just feel a bit better when hunting in places where the other hunter is a big bear, having a rifle that fires 200 to 400 grain bullets in my hands. So if I am hunting in the open plains or river bottoms and some of the mountains where no grizzlies are seen I am found with rifles from my 25-06 and up in my hands, but the more big bears are around the more my deer rifles seem to grow.