Both are brilliant shows but if we get smart and judge the show by quality, Game of Thrones is more consistently well written than Doctor Who. Moffat does a much better job that people give him credit for, but he does indeed mess up at times.
That being said, if we go about this based on preference ONLY, then I choose Doctor who. This is probably because the Doctor is my favorite TV show character ever. The combination of the Doctors good and darker side make for some interesting stories and character arcs! Plus if I'm honest here, it's sometimes amazing and fun to watch someone who is genuinely in love with life and peace to lose himself to darkness for the greater good.
Seeing the Doctor lose his temper and do questionable things is always a treat, because you know he feels bad about it, but you're also aware that he'd do it again if he had to.