They're both set in space and have fast paced action-adventure. Thats's two similarities. What else? (You said they have a lot)
I don't see how any half decent director could have any kind of creative conflict, never mind someone like Abrams.
Isn't that enough? Those elements comprise the bulk of the stories.
As I said, I could be wrong. But I won't be surprised if Abrams steps down from Star Trek after his 2nd movie to concentrate on the Star Wars trilogy.