OK, so don't get me wrong here. In a straight up one-one-one battle, Superman would win a fight with the Doctor effortlessly. The former has super strength, super speed, flight, eye lasers and a whole host of other minor abilities; whereas the Doctor really is not that much stronger than an ordinary human barring his ability to regenerate. If you give Superman the first shot, he'll win, no question.
But what got me thinking about this was the ''Goku VS Superman Deathbattle'' from Screwattack (go and watch it if you haven't, its quite fun). In it, they make the claim for Superman winning because he is always as strong as he needs to be, whilst Goku has limits. And you can prove this theory very easily with a brief skim of their respective series. Whenever Superman goes up against a superior enemy, 99% of the time all that he does to win is dig a little deeper, absorb a little more sunlight, and then proceed to kick the other guy's ass. When Goku fights a superior enemy however, he has to go off and invent a whole new transformation or fighting technique. If you don't give Goku that chance, then Goku is finished.
Going by that logic, if Superman is always as strong as he needs to be, than the Doctor is always as smart as he needs to be. The Doctor has defeated whole armies, he has defeated gods, he has won against nearly impossible odds - and all without firing a single shot. As corny as this may sound, the Doctor's brain is a WMD in and of itself.
If there is ANYONE in fiction that could invent a completely new form of Kryptonite, or could create a defence against Superman's powers, or to even take Superman's powers away from him, it would be the Doctor. And then we must factor the Tardis into this. The Doctor is too noble to just intercept Superman's spaceship unless the universe was at stake, but what about landing on Krypton, doing his hero thing, and preventing the planet from blowing up in the first place?
I think that provided Superman never had the opportunity to sucker punch the Doctor when they first meet (which Superman wouldn't do any more than the Doctor would attack baby Kal El), then you would have an endless series of attacks and counter-attacks that achieve nothing but collateral damage. Neither side being able to truly win or truly lose.