Bobcats are utterly harmless to humans. I don't think they've ever attacked even young children, unless they're rabid or something. Max weight is about 30lbs so any CCW weapon will do.
Cougars HAVE attacked and killed people for food in California, some doing so despite being only about 80lbs. They can run up to 150lbs or more and should be considered dangerous animals. That's not the same as "shoot on sight" of course, unless it's an urban area and it's been violent or is aggressive.
Most reports I've read say that cougars are not much tougher than humans if any, and can be dealt with using standard CCW weapons and ammo. There's also been a lot of cases of people fighting them off with rocks (big enough for "bashing" upside the cat's head) and any manner of clubs/knives/etc.
They're better "armed" than a dog of similar size but are actually more delicate...a bit Rottweiler or whatever is more likely to shrug off 9mm to the chest than a cougar, but a cougar can tear you up faster and is more likely to hunt you in "stealth mode". Several of the California killings involve people jumped from behind with the back of their neck or skull crushed. Do NOT run from these things, stand your ground and be ready to fight with whatever you've got...they'll usually back down from counter-aggression, yelling, etc.