Chrome is more compatible and helps to open numerous tabs in a single go without frequent crashes. They also provide various seo friendly plugins to help your website optimization.
I would say chrome is better since Google is improving it at much faster steps with Mozilla. Chrome performs faster than Firefox as fast as my personal experience is concerned.
If you are a web developer or java developer or dot net developer then you need to use mozilla firefox, it is developer friendly browser with *firebug and inspect element feature. If you are web designer and User interface developer then you can user Google Chrome because it has different types of mobile view options and very easy to check responsive web design testing things.
I like to access net using Google Chrome browser because it has many extensions like awesome screenshot, instant dictionary, responsive design testing simulator etc.,