First of all, Star Trek and Star Wars begin in different media. Star Trek is a television series (initially) and Star Wars is a film (initially). As a series, Star Trek emphasized exploration, sci-fi speculation, and mediations on humanity's place in an expanding world. Star Wars was an entertaining, action blockbuster.
So they are not even attempting to do the same work. For what it is, Star Wars is efficient, however I simply don't enjoy action blockbusters. Star Trek succeeds very well at what it does, being one of the first classics of television. As a more ponderous person, I loved it.
As to cultural significance, Star Wars primarily influenced the way Hollywood produces major action films; but this seems to me external to what one would normally call culture. On a pop-cultural level, perhaps it has been less of a niche-interest than Star Trek.
Star Trek, on the other hand, makes a positive contribution to culture and developed the television medium. Again, on a pop-cultural level, Star Trek appeals to a niche, whereas Star Wars tends to appeal more broadly.