Yes and no. Properly prepped, both Fate and Strange do pose problems for him. In a quick-draw scenario, though, he definitely has the edge.
This is probably too close to call reliably. Any of the three teams could win. Because sans meaningful prep, I think the Doctor eventually wins the magic battle. But not right away, and not 10/10, and the other WS characters are definitely a notch below Surfer/Thor. I don't see Adam being a decider, but Zoom is a tricky power set to counter. The magic users could do it, but they'll be busy with each other. So does the balanced might of Surfer/Thor make it a mismatch before The Doctor wins? Does Zoom prove uncounterable and/or speedblitz the Doctor in the opening milliseconds? Or does the Doctor eventually overwhelm the field?
So that was a long paragraph to say I have no idea. Good thread though...very close.
The question isn't quite answerable as you ask it, because it's the same character. It's a clear homage to Doctor Who's regnerations...but instead of the same mind with a new body/personality, the WS Doctor is a new person each time, but inherits the experiences and memories of past Doctors.
So the correct answer to this question is "the most recent Doctor" because they have the memories and experiences of every Doctor prior to them, and thus access to their feats and knowledge.
Or did you mean which Doctor between Fate, Strange, and WS? Then it's a matter of prep and which incarnation, with Fate at least.