This seems to be more about the algorithms of the Apps and not the hardware of the iPhone. I also run with an iPhone App as a backup to my watch (Garmin 620 now) and have 100's of duplicate runs. So far the most accurate iPhone App I have found is Strava. Hopefully Apple will work hard on getting the algorithms right on their App.
All iPhone Apps have the hardest time on extreme trail running (lots of elevation changes with close switchbacks) but Strava is still better that all other iPhone Apps I have tried (and I have tried MANY).
How accurate did you find Nike+?