Everybody knows Star Trek, especially in its prime when EVERYBODY, not just us geeky-types, watched. It was mainstream.
Dr. Who is much more niche. It may be more "popular" now in that group, but that's only because it is current. It has never been mainstream, especially world-wide, and I don't think it ever will.
I know of the 50th anniversary episode, but that's only through ads in comics and an article here or there on boards like this (where, in this thread, I just learned there is a documentary and more coming as well). If not for that, I wouldn't know about it and anybody who doesn't live in England and has never seen an episode has zero clue there's anything special coming up.