Taking a look at Doctor Strange and then Doomsday, and then taking another look, would likely make a few fans scoff at the notion that a master of the mystic arts could do anything to the unstoppable killing machine that took Superman down back in the 90s. But if there’s anything that’s been learned about comic book characters over the years, it’s that their greatest strengths come from both plot armor and the abilities they’re given, and how such advantages tend to evolve after a while. Doctor Strange has been a potent character since the early days, as has Doomsday, but the startling contrast between the two characters, in a physical sense, is enough to make a lot of fans wonder why this battle would ever take place. The easy answer is that people just want to know, which is why a lot of hypothetical battles are concocted to see which way people will swing and how many different instances will be brought up in which this character did that or that character wouldn’t be able to counter one power or another. There are obvious mismatches out there, but this isn’t one of them.
Doctor Strange can’t match Doomsday’s strength, but he has other methods of fighting.
A fight to the death in terms of physical strength would leave Strange as a bloody stain on the ground when going against Doomsday, but with the kind of power that Strange wields, it’s easy to see that he wouldn’t even need to get close to the creature in order to have some effect upon him. From his use of the mystic arts to the artifacts that he can call upon and even just the fact that he can open a portal pretty much anywhere he wants with a sling ring, Doctor Strange has a ton of advantages against Doomsday. His most damaging spells would slow down the behemoth, at least, but it’s fair to think that a lot of what he can do wouldn’t be quite as effective as some would like to think. The truth about the gray-skinned beast is that he’s been subjected to so many different types of damage that he’s nearly impervious to anything that can do physical harm, at least to a degree. But to Strange, that’s a minor hurdle.
Doomsday isn’t exactly an intellectual being.
Giving credit where it’s due, Doomsday is an instinctual creature that knows how to process information, but in terms of being a villain that can outthink his opponents, he’s far below Strange when it comes to intellect since the Sorcerer Supreme can think of multiple ways to take Doomsday down while the bony creature is going to be thinking of smashing Strange repeatedly until he’s nothing but broken bones and flesh. With so many attacks he can consider, though, it’s very likely that Strange will make use of one or more spells that will help him to gain and maintain distance from Doomsday while trying to think of something that will put him down or incapacitate him for a much longer period of time. From using portals to keep the creature at bay and off balance to the mirror dimension and many other possibilities, Strange would keep Doomsday guessing and would also be trying to keep him away from civilians as much as possible. Transporting him to one hostile dimension or another might be kind of interesting.
There are so many different ways that Strange could simply exile Doomsday or confuse him.
A fight between Dormammu and Doomsday might be interesting since the ruler of the dark dimension has given Strange numerous problems over the years. Plus, Dormammu is the ruler of his own dimension, so whatever Doomsday does isn’t bound to be enough. But that’s a mismatch for another day since the truth is that Doomsday is a physical combatant and both Dormammu and Strange wield enough supernatural force to take the creature down or at least bind him in various ways that would negate the power that he holds within his immense form. Given that it’s been stated that entropy is one of Doomsday’s only real weaknesses, which means that at the end of the universe and the end of time, he can be destroyed. But since that feels like an extreme measure, it’s far more likely that Strange would find a way to bind him, at least for a while, since his strength is such that he might just keep coming back.
In the end, Strange is the more versatile character.
The mirror dimension might actually be one of the best attacks since, without any magic at his disposal, Doomsday could be trapped, and no amount of punching is going to release him unless he knows something his creators don’t. So, in the end, Doctor Strange takes this fight the majority of the time since as long as he keeps his distance, he wins ten out of ten times.