I didn't let mine die completely, I don't know if that's the difference? My first day with the phone I was probably on it... screen on and fiddling with it... for a good majority of the day. I'd say at least 6 hours? (please don't judge, it's my very first iPhone!) It was probably on (standby & operating) for about 9 or 10 hours total throughout the day of first use - No charging straight out of the box - until I got a 20% warning. I charged it up last night and yes I did find the same thing today - it's pretty solid for me and how I use my phone, but I did expect a little more out of the battery.
As far as the Droid Razr Maxx battery life and best phone opinion - my husband just upgraded to the Razr Maxx and gets about the same battery life out of his Maxx as I do my iPhone. It does last longer, but not by much. He plays a particular game a ton - so I'm sure that takes more battery life too. Both appear to be awesome phones so far, although we have big problems seeing the screen on the Razr Maxx when outdoors. That's our biggest complaint with that phone. 
Having a New Device is Exciting 
and Letting it out of your Hands the First Day is almost impossible. But i guess on my First Maxx the Reason i Hooked it Up and Charged it Fully and then done the Rest of the Steps then Enjoyed it is because having prior Devices and how i Done with them. It was second nature take care of important stuff then enjoy it.. but it was Hard for one it was my Present for my Birthday. But once i got the important stuff out of the Way i hooked my Maxx up to Winamp and put the Metal to the Pedal i streamed a straight 22 Hours with out one skip or stutter. And i still had about 1 hour of battery Left before i had to Hook it Up..
