In Australia, Doctor Who, I would guess is the bigger of the two.
It's difficult to compare : Who
is shown on the non-commercial ABC and has been an after-school staple for generations of Australian kids. Since the re-launch several years ago it screens on weekends at night, and has never been taken off due to lack of interest.
On the other hand, all the Star Trek series have run on commercial stations here, and none managed to find a big enough audience to make them viable as a prime time option, so all were banished to late nights. You would need to go back 35 years to when Star Trek (TOS) was on during primetime here.
It's hard to compare revenues as well. This year Star Trek Into Darkness
made about $470m USD worldwide. Last year BBC Worldwide (which you would suspect earns about half its revenue from Doctor Who), made $1,808m USD.
In terms of shelf space, Doctor Who wins here, no contest, there is aisles of merchandise. There is a lot of buzz around the 50th anniversary at the moment as well.
Anyway, it's hard to say, but my guess is Doctor Who would win the popularity contest here, mainly because it has been a lot more accessible to Australians over its long life than Star Trek has.