An interesting question. Star Trek started at the bottom and went on to spawn a media/merchandising empire that created more series and movies based upon the original. Star Wars started at the top a a media darling in the movies and then spread backwards into other avenues.
Each came along in very different cultural time frames in our society. Star Trek was introduced at a period where man was just beginning to probe space and look beyond earthly sentience. It explored racism, ecology, politics and sexism. It espoused technologies that were just being dreamed of that eventually came to fruition.
Star Wars came along in a society that was already aware of the grand ideas that might exist beyond our planet. It is not to hard of a jump to find similarities in the Old Western Movies or some of the Aurthurian Tales.
Whereas I have a great deal of fondness for each series I think Star Trek had the more profound effect on our society.