After spending a lot of time testing various android devices I can say that there are a few things that android does that I wish the iPhone did. The number one thing I would like to see Apple tackle is better use of the lock screen and notifications.
On all of the android phones that I have used, I have been able to simply glance at the lock screen to see if I had any messages or alerts. Very nice. On my iPhone I have to unlock the screen to check for anything new. This was the main reason that I checked out jailbreaking a while back; the things that you could do with the lock screen were nice, but I decided that I would rather not be jailbroken so I went back to stock. Better use of the lock screen would make the iPhone more convenient.
For overall notifications I like the way that android handles things via the notification bar at the top of the screen instead of how they just popup on the iPhone and overwrite each other for things like calls, texts, etc.
These are a couple of the things that I would like to see improved in a future version of iOS but I won’t hold my breath.