The main characters backstories are different, the ships and settings look different, the way the stories progress are different. In a nutshell, Nero was the vehicle for being able to state that ST:09 was a reboot by creating this "alternate timeline" - in any regular episode the timeline would be restored and the continuity "reset" back to the way it was before.
So the lack of episodic TV-style reset is the reason it's not Prime? I don't buy that. Sustained cause-and-effect means it is Prime.
I'll just mention the example of Eureka, a sci-fi show that altered its timeline in the middle of its run but remained in the same continuity. Can anyone think of other examples?