Chrome for speed.
Firefox is a little more reliable across a wider range of sites, especially when it comes to authentication. Like there are a couple chatrooms I use when I watch sports. Chrome kept logging me out. But Firefox was rock solid (so was IE). Chrome failed me when it came time to redeem a code at a website. I ended up having to go through customer support for hours to tell them that the redeeming process didn't work and I never got the product but on their ends it says I got it. I did read in forums that they had a similar problem with the site with Chrome but not FF/IE. So my second go-around with a different code worked perfectly in FF.
Plus, Firefox has all the cool plugins. Chrome is getting better about that but still not as good.
That said, the speed of Chrome makes up for any idiosyncrasies. I've decided for my basic browsing, I'm using Chrome. For anything with money on the line, I'll use Firefox.