Polar bears will in fact just kill you and eat you. Grizzlies, very likely to be territorial. Black bears are the most “cowardly”, but all three will fuck you up to protect their young, hence why the season matters.
I haven’t exactly done the math on relative bear populations to tell you if your odds are better with a random bear or a random man, but it doesn’t matter, you wouldn’t consider any of my statements valid even if I wrote a whole ass thesis.