I don't own an S4, so I can't speak from personal experience, but this is what I'm thinking:
Nexus 4 - 2100 mAh battery - my average screen time is 4hrs
GS4 - 2600 mAh battery - if you get anything less than 4hrs screen time, one of three things is probably happening:
- you have everything on and full brightness
- you are spending most of your times on games
- you have a defective device
I am highly inclined to agree. Another question to all who have an S4: Do you have Auto Brightness on? That feature is nice, but a battery killer. It frequently tests the ambient light and adjusts the screen brightness to accomodate.