I think 4 hours is normal if that's only screen time with data on. I can easily pass 4.5 hours of screen time with WiFi and sync on, standard battery. (At least, that's what I got when I was addicted to "Where's My Water" and "Cut the Rope." Hehehe...)
For my normal usage though (lots of calls and texts, sync on, and a little bit of web browsing and Foursquare), I got 2h 18m screen plus 4h 2m voice calls in a span of 2d 7h before ending up with 4% remaining. The extended battery adds either ~1 hour (screen) or ~2 hours (voice) more to that.
As for the signal... My GNex is significantly better than the S2 for 2G, since the S2 drops the signal from time to time. As for 3G, not so much. Still difficult to get a signal from where I'm sitting, except when I stick the phone out the window, but who does that?