Yikes! Long ramble ahead.
Best knife against a bear? The only way I could see to quickly disable the beast is to go for the neck. The eyes are an inviting target, but blinding the beast could just as easily drive it to new levels of frenzy as put it out of the fight. So you want something slender and narrow to penetrate deeply through all that fur and flesh, and then slice viciously. You're not batoning here, you don't need a quarter inch chopper. This is where you want a fine, thin, serrated edge. Rainwalker's AK47 might get job done, but you'd have to an accomplished swordsman I think to land some good hits without the bear grappling you. Because once the bear is grappling you, you're done. I don't care how pumped you are, the bear weighs twice what you do and is vastly stronger.
A spear would be preferable to a knife if you were limited to hand weapons, as it allows you to both keep your distance while attacking as well as receive a charge. But now you're talking about either carrying a spear all the time, or being able to fashion one within seconds from materials within arm's reach.
Quite frankly, I'm thinking if you're down to fighting a bear with hand weapons, you're already done. If I was in that situation I would of course make an attempt but I wouldn't give myself good odds.
I have a few friends in Alaska who do the 12-gauge-with-slugs. Some prefer a rifle. I hear .30-06 with soft points will probably do the job (after all, you're taking a frontal chest shot, the bullet is going to have a chance at every organ they've got). But what you really want is a .45-70 with big (400 grain) flat or hollow point. Which is basically doing the same thing as the slug, going for maximum impact and wound diameter at the expense of penetration and range.
Either way, long guns are definitely the best route against anything bigger, stronger, and faster than you are.
Wild cats are a different matter. A bear (except polars) will not attack you as a food source. They would much rather dine on things they don't have to fight first. It attacks you in defense or because it's rabid, which basically means once you're engaged it's either you or them. A big cat will definitely see you as a food source, and as mentioned above cats are ambush predators. They love to pounce from behind, which makes that rifle shot difficult. However, cats are also pragmatists, and will disengage if you're putting up too much a fight. Thus do not play dead. Because the cat, unlike the bear, will eat you. <img src="/ubbthreads/images/graemlins/smile.gif" alt="" /> There are survivor stories about outdoorsmen and joggers (running equals "Attack me!" in cat-speak) who drove off cougars and the like with a vigorous defense. The cat, figuring there must be easier prey elsewhere, left them alone.