Compatibility issues isn't really Google's fault... and I have seen very few compatibility issues. A lot of websites fail at the compatibility crap because they do manual, hard-coded checking (if it's IE, display this, if it's Mozilla, try this), and they leave out the idea of "what if a new browser comes along." With most other browsers, this doesn't affect them, because a lot of "new" browsers are just clones of old browsers; Chrome is genuinely new.
Having said that, I use Chrome a lot; it's great for developing, and I just fine it's generally faster (app speed not network speed) than Firefox; Firefox sometimes takes up to 300k in memory... I can live without that. (Still, my second choice is Firefox)