Both have selling points.
When I was young, and went to see the second and third Star Wars films in theaters, it blew my mind, all the toys and such were all over my neighborhood and we would play out our tiny epic battles in the empty lot at the end of the street.
I had always watched reruns of original Star Trek with my father and TNG in the late 80's/early 90's as well, so I also have some fond memories of that story too. The films were pretty hit or miss, with more bad than good really (I still like Star Trek IV though, as goofy as it is), but the recent Abrams one was fantastic and, for me, definitely trumps any recent Star Wars film.
So, I have to say that when younger, it was definitely Star Wars, up to about 23. After that, Star Trek kept my attention better, as it is primarily about the relationship between Kirk, Spock and McCoy, a smaller story in a huge world.