Large cats are not hard to kill, at least those in the US. Many years ago I took a pair of foraging cougar in Colorado with a 357 magnum using 125 gn hps and broadside shots. I also took a Jaguar in Central America, but used a 44 magnum on that one.
Some guides I have read about use dogs to tree the cats and a 22 magnum to take them.
However, that being said, if it is a one on one situation and you happen to be blocking the way out for a large cat, you will need enough gun to stop them or they will use you for a launch pad and their claws will tear your butt right up.
If I was to go out again looking for large cat I would use any of the magnum calibers just to be safe. HTH. Mikey.