While Dr.Fate has more exp., Dr.Strange may have more artifacts, and The Doctor can change reality. Doctor Fate seems to have powers similar to that of a green lantern. I don't know. I don't have that much knowledge of The Doctor. But, Doctor Fate vs Dr.Strange may possibly be a stalemate.
True enough. Time travel is nothing for the Doctor, and he could potentially match anything else they do as well. With a good writer (or a good showing) he's well beyond Skyfather.
Doesn't always work. I know you like it, but Strange has blocked the reality-warping properties of the IG. Do you really think the Doctor's beyond that? He isn't. But he has enough varied options that he'd win the fight anyway most of the time.
But he has time traveled, TK'd giant buildings into space, grown himself to the size of a skyscraper, and done all manner of impressive things without tiring in the least.
Name one other time besides stopping time where he was weakened from a spell. It happened once in the Relentless arc, and it was the first time he ever used his powers on a large scale. Other than that, there isn't an instance of it....ever. So if he sticks to what he knows, he won't get tired and he'll win more often than not.