I really enjoyed both shows and watched them both the whole way through. If I have to choose one, I'll choose The X-Files
. I was an obsessive fan in my teenage years, jadedly followed it right to the end, and can still pop in a DVD and enjoy a classic episode.
As others have pointed out, XF could tell a huge variety of stories involving a wide array of subject matter (from somewhat-plausible fringe science to totally fantastic otherworldly weirdness). I do think the lighter tone that developed around S6 took some of the show's original intent away, but it obviously needed to make some changes to survive.
I think both shows did develop some problems - XF got too wrapped up in the convoluted conspiracy arc, and basically went on for far too long; and Carter specifically wrote some terribly pretentious material in the later seasons (I applaud Duchovney and Anderson for going through so many flowery monologues without stopping for breath).
was fantastic too, but personally I didn't agree on some of the directions the writers took. I don't like the "soft reboot" from the beginning of S4, or the Observers turning out to be Nazis. Also, there were some interesting plot elements that could have been handled better (e.g. I would have liked to see more regarding the Cortexiphan experiments and their subjects).