They stay present in Notification Center on the iPhone as well.
The problem with notifications moving off the lock screen and to the notification center is that they remain out of sight and then out of mind.
I prefer how on Android the notifications are always in your face - you keep the ones you care about and get rid of the ones you don't. On iOS, the notifications I care about are often hiding under dozens of notifications I could care less about. I can't tell you how many times I find a notification in their I wasn't even aware of and to make it worse, I have to make a conscious decision to check notification center so it becomes a chore.
I think Apple could do a lot here to improve the experience.
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