My wife has the S3, I have the Nexus. One thing I can tell you is, the S3 battery is 10x better than the Nexus. She uses her phone very heavily and still has battery when the day ends. I barely use my phone and its dying by 8PM every day.
She is experiencing one issue. When connected to our home wifi network, every couple minutes a notification flashes across the bottom of the screen saying "Connected: Home Wifi Network". Anyone know how to turn this off?