This is just from my personal experience
Chrome
Pros: Nice google integration ability (obviously), a stupid high amount of addons and extensions; lots of customization, downloads are managed well, decent HTML 5 integration.
Cons: Eats up ram faster than a fat kid eats cake at a birthday party.
Firefox
Pros: Good amount of customization, good built in security features
Cons: Some compatibility issues with certain machines, eats ram (just not as bad as chrome), can sometimes have trouble with HTML 5