Star Trek had the more diverse universe and actually had some interest in developing those cultures as the series went along. What annoys me about Star Trek though is that ships always seem to interact as if they were constrained to a 2d plain.
Star wars is more so about space mages and space cowboys fighting it out in a universe which seems a little too consolidated to start with. Empire/Republic... else we have little back water organizations on the outskirts of the galaxy such as the trade federation or the cloners... and they all get wiped when the empire takes over the republic which spans the galaxy in a single day. Additionally star trek tried to have some sort of coherent history where as from the old movies to the new movies (about 20ish years since the new ones end with Luke and Leia being born) the force goes from being a scientifically explained bacterial reaction to being an old superstition (to paraphrase Han when Obi Wan is telling Luke about the force on the Millennium Falcon.
The movies don't explore much about the outer cultures, yes the story is centralized in the Republic and Jedi, that's the main plot, but there's a big universe out there, explored in comics or books.
ST and SW have different concepts, one explores the universe the other already has a base of universe. I'm not sure which series is more extended in cultural exploration, this counting with those books and comics and whatever else Star Wars haven't show in the movies.
In example, StarWars has allot of 'domestic' animals, like we have horses, and i don't remember much diversity of that in Star Trek. SW also have botanic references, explored in StarTrek but not as defined. I think LucasArts made a game about species, you have a zoo and botanic garden to take care of.
That's why I'm waiting for SPORE, i wanna be GOD! Hey i gotta make a topic about that.