Well the recent star trek movie isn't based on the setting that the crossover takes place on. It seems like I could be interested in star trek in a general sense, but I never really got into watching either star-trek series. I reckon it was something that just existed outside of being exposed to the generation I belong to.
I did see wrath of khan recently, but all I got out of that movie was how much other TV shows love to drop a reference to that specific movie.
Dr Who on the other hand, I have seen a lot of the recent episodes that have come out. But I only watched those to confirm without a doubt how much I loathe that show on just about every conceivable level. Yeah, I have only seen that one guy portray the Doctor, but based on the very idea of who the doctor is, I am pretty sure I would hate that guy above all other guys regardless of whoever happens to play his part.
I reckon I do not disagree with the show on the basis of it being a fantasy series, so most of my loathing must stem from the concept of a show set up like that one being widely considered as something that qualifies to belong under the category of "science fiction". Basically it takes pretty much every single aspect of that particular genre that I personally love, and goes the exact opposite direction with it.
For instance, even if I operate under the assumption that the self preservation principle employed by the Angel species in that series has zero correlation with actual quantum physics, and the Doctor just calls the state "quantum lock" in order to give a familiar analog to explan the idea properly to dumb humans, I could still go on at an absurdly extensive length about now there is absolutely no aspect of that species that makes any practical sense whatsoever from a survival/evolutionary standpoint. The way I see it, the very concept of the Angels at it's every core, can serve as a perfect metaphor for the very nature of how I could never tolerate much less accept that show ever being considered a work of science fiction.
No Dr Who, you cannot use the basis of the main character having an inheritley higher level of intelligence than any conceivable member of the show's audience as a golden ticket that gives you free reign to have anything happen in any way possible. All you are doing by claiming it doesn't have to make sense to anyone else as long as it makes sense to him is only accomplishing is a setting where the entirety of human effort and development (that he 'loves' so much) are founded on nothing more but complete lies.
If you want a metaphor for that, its as if the Doctor personally equates anyone believing in any aspect of reality as anyone ever knew it, as the same as a child looking at a puppet and believing they are witnessing the actions of an actual person. Even if I was willing to accept that kind of grim, lovecraftian premise, it still means that every single motivation the Doctor has ever had for placing value on the human race itself is a blatant contradiction. From my perspective, it is literally impossible for that show to ever make sense regardless of how anyone can interpret it.
In short, I can never tolerate the concept Dr Who as science fiction, in the same way that Einstein could never tolerate the concept of Quantum law as science fact. (which is ironic, because I am actually a big fan of quantum law. If you are going to make a show just for the sole purpose of me personally hating it, then I appreciate you taking the trouble to shit all over the basic principles that allow that field to operate for the purpose of nothing more than to generate 'dramatic effect')