The battery is so thick that the S4 to my measurements with the attached new backplane is 14.7 mm thick - almost every one of my friends spoke to me as to why I have my S4 so missed an ugly "shell".
No matter: I use the S4 quite intensively (mostly offline), and the standard battery is never much more than a day; last weekend I have to anchor battery disconnected from the charger on Friday afternoon and Monday morning were still 12% residual capacity available.
I'm excited.