If you had asked this question before 2005, I would definitely say that Star Trek was more popular world wide, in terms of its presence in popular culture, and general awareness. Star Trek left television right around the time that Doctor Who was returning to television, which is pretty much the reverse of what was happening in the late 1980's. Now Doctor Who has a new series going, and has had a new-found resurgence in popularity, because it is regular and current. We are getting 13 - 14 new episodes per year plus specials and spin-offs like the recently ended Sarah Jane, or K-9, so Who is a very hot thing right now.
By contrast, it seems we are getting a new Star Trek movie every 3 - 4 years, so it does not have nearly the overall presence of Doctor Who right now. Both are certainly the two greatest Science Fiction screen franchises, with both having roughly 50 years of history and are still going. Sure, Trek went away for a while after 69, but we still had the animated series and various novels and comics during that time. Doctor Who left TV at the end of the 80's, but we still had books and audio dramas. Both franchises survived their hiatuses, and I believe that Star Trek will return to television again some day. When Trek finally returns to TV, we could see it once again matching the popularity of Doctor Who, if it is done well enough.
Remember that Doctor Who was off the air for 16 years, and it has only been 9 years since Enterprise ended. Star Trek spawned 6 television series, 12 movies, had a space shuttle named for it, and has had numerous real world technologies inspired by it, so we can't forget about all of that just because Doctor Who is more popular at the moment. Personally, I wouldn't mind a revival of Star Trek Enterprise, or a new series about Worf.