It just seems like there would be a conflict of interest. Perhaps I'm wrong. Logistically of course he could direct both. I was more referring to there being a creative conflict. While not identical, both franchises have a lot of similarities. I found Abrams first Star Trek movie to be reminiscent in parts of Star Wars.
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.