Yup, Star Trek all the way. It's a much more recognized global 'brand'. Doctor Who was always a niche (even in it's home country, even in the "classic era" of the Tom Baker Doctor) that was kind of a cultural phenomenon but never, I'd argue, a global brand. Heck, it was broadcast in loads of commonwealth countries, but it just didn't have the market penetration of a Star Trek.
Granted, the revived Doctor Who series that has been running since 2005 has gone a long way to rectifying that perception. Even in it's home country (especially
in it's home country?) Doctor Who was always seen as something of an embarrassment, a well-known, but not well-regarded, programme that was often written off for what it wasn't rather than being praised for what it was. That is, until
the 2005 series came along. That's when Doctor Who *really* started to become a global brand to be reckoned with. But that's recent history. Star Trek was way ahead of the game on that score.