For me, .357 is for a K frame and above. J frame revolvers that can shoot .357 are good in theory for if you HAD to, but they generally excel at being a touch heavier when you talk the difference between something like a 642 and 640 so that shooting .38+p is more comfortable.
.357 can pack a wallop when loaded up. Lots of blinding flash and report with impressive ballistics. That kind of power, for me, handles better out of a heavier gun. Even still, it's not my go to for probable low light situations like bump in the night work. It's bright!
So, for me, small j frame size guns are .38s. I shoot .38s in .38s (obviously) and .357s in larger .357s. That said,. 38+p is no slouch. It's not a bear gun, but I dont think even .357 would be my first (or even third) bear gun choice no matter the barrel length. What it is is a good all 'rounder that can do in a pinch.
The .38 would be enough for a cat, if you get a bead on it before you know it's on you. Big cats around the states are cautious for a reason. They aren't armored with thick fur, fat, or muscle. They are large and strong, but poking holes in them isn't difficult.
Good luck