How much internal storage for apps does Nexus 4 have?
No device can have all of its internal storage free for user. The Operating System (and pre-installed apps) needs some space for itself. So Nexus 4 doesn't give you 16 GB free either.

The 16 GB version of Nexus 4 gives user an approximate of 12.92 GB free. Whereas, the 8 GB version of Nexus 4 gives you an approximate of 5.67 GB free space to use.

I don't have the device (at least yet). This is what I have found in reviews / discussions.