Honestly, I have an older computer, if it comes to just surfing the web Google Chrome comes in handy but when starting to use things like YouTube, Firefox. It seems Firefox handles the scripts better than Google Chrome. I have 512 mb of physical ram, 400 in which can actually be used. With Google Chrome, I easily have 100mb of ram being used just for back processes and then anything else, I don't that with Firefox.Both are great, I prefer Chrome's style over Firefox but Firefox with add ons = win.
i would have to say that they both have thier perks. chrome is by far the fastest and easiest browser to use. it has more plugins now that it has been out for a while. google chrome also has a very nice customizable interface.
on the other hand you have firefox. it also is quite fast and easy to use. i did notice that they coppied chromes interface tho. the main reason you will see people get firefox is for all of the plugins. there is such a vast amout of amazing pluggins.
in my opinion chrome wins by a mile. also i have to say that chrome has unlimited funds and will always be moving foreward. firefox would be my second descicion tho. but honestly i think any browser is better that internet explorer.