I say use whatever browser you use on your computer. If you use Chrome, use chrome. If you use Firefox, use Firefox. if you use Opera, use Opera. If you use Internet Explorer, kill yourself or get another browser.
Basically, Chrome, Firefox and Opera mobile are all fantastic browsers for the phone, each has their upsides and downsides but they all can sync bookmarks, tabs, searches, etc with their desktop counterparts. So use whatever you use on your computer-I like both chrome and firefox on my phone but mostly use chrome because it has a great UI and runs really well.
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