Meh, Dr Who's just far too silly for me - can't take any of it seriously. Watched the Christmas episode; 'stay out of the shadows of they'll eat you!' 'oh no, the shadows are making a space suit attack us! Really slowly!' bah ;P
As to Trek vs Wars, both have their major failings.
I grew up on TNG, and then Voyager, and loved them both, but looking at them now the acting is pretty horrible, the situations have fairly predictable endings, and they pretty much always carry a message of personal improvement - war is bad, generosity is good, stand up to evil, if in doubt use the deflector array, etc. Voyager went a bit further if I remember right, with having to make some difficult decisions in the quest to get home, which was nice. Didn't seem much of Enterprise, but I liked the modern CGI.
In short, although Trek had some good persistent characters, occasional interesting situations, and long sub plot arcs (in a sort of Borg in the back ground kinda way...), the simplicity of the general moral decision and the common resorting to technobabble to save the day pissed me off a little. Unless the cgi was good, heh.
Wars I initially loved, back when I saw the first episode and all that. However, watching it again makes me realise just how thin the story really is, and just how bad the majority of the line delivery and writing was. The whole thing is just farcical outside of the battles and sections without dialogue. And even in the battles... well, Ewoks? Were they seriously just there for the cute factor? Did their slings seriously injure the troopers though their body armour? Bull. And then Episode 1, another excuse to throw a silly alien race up against the evil military force, but this time they weren't even cute, and there weren't any actors involved. What a cop out. Not impressed.
However, considering how poor the execution of the source material was, the Star Wars franchise has made some nice games - Rogue Squadron was awesome, I played Jedi Knight, I enjoyed Pod Racer (heh

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Summing it up, neither franchise is awesome, though I'm praying that the new Trek movie doesn't suck... really want to enjoy that. Both have had some good and bad games made from them - Star Trek Armada I & II, Elite Force I & II against Rogue Squadron series, Jedi Knight series, Force Unleashed to name some of the better ones (imo). Both's sciences rely on you not picking too closely at how they work, though Trek makes FAR more of an effort to at least put names to its brands of magic. Which you prefer depends entirely on personal preference, and can change over time, so picking a side is closed minded and petty, tbh. There's better sci-fis out there - Firefly for sheer awesome win, Red Dwarf and Hitchhiker's for comedy.