I rooted just to put the stock AOSP browser on my Nexus 7 because chrome was running like crap for me. A bunch of pages I go to would lock up and become unresponsive while things were loading. When it's done loading it's fine but I was getting pretty annoyed. I haven't tried chrome yet with the custom ROM I'm running but the regular browser is running great just like it always has for me. I had this experience on my GS3 too, the stock browser has always been by far the smoothest for me, +it can run flash and the quick controls are pretty cool.