I use the ZeroLemon 7000 mAh extended battery so not really a fair comparison to the stock S3 battery. But I usually have about 45%-50% at the end of the day (7am to midnight).
I usually charge every night but could go two full days on a single charge if I wanted to.
My screen on time is about 5 to 6 hours a day. When I was breaking the battery in I had to force it to die and had a couple days of 7 hours of screen time.