Well...
You can't say one is better than the other because
and Star Trek are not even in the same galaxy with each other (literally). One is basically a dude that runs a lot and tries to keep the humans safe and murders a lot of other alien species in the process and the other one is a space show about exploring and fighting alien races to save the UFP (United Federation of Planets) ((holy cow I'm good I remember that lol).
Kirk/Picard/Janeway/etc can die... the doctor can't (anymore for a while... unless he's killed twice in a short period of time basically).
Doctor who always has Christmas episodes... how cool is that? Pretty cool.
Doctor who has scarier villians. If the Borg met the
Dalek I'm pretty sure the Dalek would win... I mean the
Cybermen are basically the Borg anyhow (assimilation = ultimate upgrade) so they really already killed a bunch of them on the show. Though I'm not sure as to why people are afraid of the weeping angels (of which we should have an emoticon). They don't actually kill you they just send you back and time and feast on the energy released when they do that... so less pollution and you know who is going to win all the wars... how is that so bad.
Cyber Leader: Daleks, be warned. You have declared war upon the Cybermen.
Dalek Sec: This is not war - this is pest control!
Cyber Leader: We have five million Cybermen. How many are you?
Dalek Sec: Four.
Cyber Leader: You would destroy the Cybermen with four Daleks?
Dalek Sec: We would destroy the Cybermen with one Dalek! You superior in only one respect.
Cyber Leader: What is that?
Dalek Sec: You are better at dying. Raise communications barrier!
("Doctor Who" Doomsday)
Startrek has a spaceship with no bathroom (I actually have a pretty solid theory on why)
Startrek has Kirk getting the green women (and boy did he)
Startrek had DS9 (I hated that show... so that's a negative for me)
Startrek said if you give the keys to a woman she'll get lost... in the Delta Quadrant.
Startrek has Picard... "Make it so."
Startrek has Geordi or should I say Levar Burton who everyone loves because he is cool as hell and is bringing back reading rainbow... see he really can do anything.
But...
Doctor who had K9
... a robot dog that was more intelligent than one of the humans that was helping the doctor.
Doctor Who had Donna though (I hate Donna... I wish she would have fallen into the volcano in Pompii (Donna was there with the Doctor))
For special effects Star Trek wins out... Doctor Who doesn't waste money on things like cool explosions...
See... they are universes apart but both are EXCELLENT (now release the hounds
)