They are both great phones. You might as well as "Which religion is best?"
.. and this is an Android religion forum, so no surprise that everyone's going for the N4
I have the N4 and my missus has the iP5. As the OP states, the iP5 is better built (though steer clear of the black one as the paint on the rear cover chips too easily), has a marginally better camera, better battery life (doubtless partly due to the smaller screen) and may have some better apps available.
If you're bought into the Apple world, then the integration with the iPad and MacBooks is pretty good, e.g.: as soon as you get onto WiFi, photos from the phone start popping up on the iPad. I'm sure this can also be done in the Android world, but I'm guessing isn't quite so seamless.
My missus is very happy with her iP5 and absolutely loathes my N4 (as she did with my previous 'droid)
To me, on the other hand, the iP5 just feels a bit 2 years ago. Whenever I use it, I find the screen laughably small and the interface as dull as ditchwater (though it works fine). Also, a deal breaker for me all on it's own, is iTunes - a total POS on Windows, though my missus seems to manage OK with her Air.
The iP5 also doesn't do mapping so well - even though the missus uses Google Maps and it now has turn-by-turn, it's simply not up with Android version. I've never seen her use Apple maps.
And Siri? Worse than useless.
For me, though the price of the N4 is the killer. Much as she loves all things Apple, if my missus actually had to pay for her iP5, iPad, Air etc, I can pretty much guarantee she'd have an N4 - we're both equally tight
