According to me Mozilla Firefox is the best browser, Because it is support most of the famous and best add-ons of SEO, which is very useful to work on SEO. In the Firefox many types of the best and useful add-ons are available, which is not available in the google chrome. like as quirk SearchStatus, Linkclump, Copy URL Expert, rank checker and etc. These add-ons are available in the Firefox not in google chrome. So I think Firefox is the best browser for any type of the work.
I actually use both, I think they both have their own pros and cons so having each available can at times be good.
For Mozilla, I would say WaterFox is the best one out there. But if you're comparing FireFox to Chrome, then I would choose Chrome.
I think they both have advantages over each other, though lately I've been encountering more errors and crashes with Firefox. Chrome's rise has been madly successful though, take a look at its market share compared to other browsers: http://www.statista.com/topics/1001/google/chart/1438/browser-market-share-since-2008/
Definitely Chrome. The multiple-profile function is very handy when you have a separate email for university, a separate one for family, a separate one for social networks. It's possible to combine multiple profiles in Mozilla too, but it's just much, much, simpler in Google Chrome. HOWEVER, Mozilla does have some add-ons that aren't available for chrome. For example, chrome has more add-ons that make YouTube better, while Chrome lacks in that departments. That's not reason enough, for me, personally, to switch to Firefox though.