I've replaced my iPhone 4 battery. It's very simple but you need a special tiny screwdriver. I have some from microcenter or you can order a battery that comes with one or order it separately. I also replaced the back with one with a design. Mine cracked and I was going to get a standard black but saw a cool white butterfly one. I'm sure you could do it to the s3 too. Just in case that even matters to you.
My iPhone battery also charges pretty fast. Seems to be much faster than the s3.