Well, Star Wars can't help but "win" because it's a fairy-tale universe where the technology is basically magic. Star Trek is at least nominally a humanistic universe bound by the laws of nature. Granted, a lot of ST bends the rules so much that there's little distinction anymore, but it's a rather pointless comparison, kind of like asking whether Sherlock Holmes could beat Harry Dresden. At most, it's an intellectual exercise, not something that should really be taken seriously.
I've got a friend who swears up and down that 'Doctor Who' and 'Star Trek' are as 'scientifically inaccurate' as each other. He said that once you are going FTL and beaming things and replicating things you've basically already entered fantasyland, and all the crazy thing the TARDIS does all occupy the same degree of make-believe. I think you can still have degrees of suspension of disbelief, that Star Trek at least TRIES to respect science, whereas Who (particularly New Who) basically handwaves magic as science and that's that.