Starwars is just a show about something in space and its not even that good to me honestly. Doctor who goes to future and past to show us what it is like to be living or live beyond the earth is going to possible die at some point while doctor who takes us all around the universe star wars teaches us nothing.
I have always been a fan of Doctor Who and have to side with that series for this argument. While a fan of both, I have always seen Doctor Who as better acted, more heartfelt, more thought-provoking, and better able to generate emotions from its audience than Star Wars. Doctor Who has a wide fanbase because of its ability to connect with viewers and make them care about the fleshed-out characters that they grow to love.
Both franchises are brilliant, but I think Doctor Who is slightly better. The realpolitik of the Doctor's character can be really in-depth and meaningful, and the infinite setting possibilities means that it has arguable the most diverse range of sub-genres of any single TV show. The thing that finally cinches it is that the acting of the protagonists is almost universally fantastic, even more so than the high standard seen in Star Wars.