Part of what makes The Doctor compelling is that they don’t always do the right thing, or even try to. They’re an interesting character study in every incarnation, but their flaws help define them. The better man is Superman.
We saw, especially with the Tenth Doctor, that without a human companion to ground him, he is prone to “go too far” and get drunk on his own power and ego.
That being said, I’ve been a fan since watching Tom Baker as a kid and LOVE the show.
There are several, in fact; they are a lot like the Trek ones, really interesting and deep dives IF you are deep into Whovianism but as an agnostic to that religion, mostly way too esoteric for my taste. I only know they exists because I got into it at an Orphans for Thanksgiving pot-luck one evening with several visiting Brits and other out-of-towners, and we had to look up who was right on-line.
I think @HubCityQuestion is correct - as far as the Doctor’s Flaw (at least for the Doctor’s since the reboot since those are pretty much the only ones I have any real familiarity to) and for as much as people want to view Clark as someone that needs to be written with flaws or deeply troubled or somehow tasked and brought down to make him appealing to modern fans, that’s not really something that works - even with the evil Superman stories - because of the choices that Clark always has made and always will make.
So I fall on the same side as @TheTerrificToyman and @moro - the point of Superman is that he will always make the best of all possible choices.
Ergo, Superman is always inherently better because of this, notwithstanding lazy or unimaginative writing that tries to imply the contrary.
He still makes mistakes and fails sometimes. Otherwise, the stories wouldn’t be as good. However, Superman’s mistakes and failures are not realistic and yes, I DO understand I am talking about an alien that flies around in blue spandex and red underwear. Despite what most of the stories show, it’s impossible to save everyone, even for Superman.
The Doctor, on the other hand, always weighs the choices and picks the best, but refuses to go through unless the people he’s with all agree. He knows he can’t save everyone with him, so he focuses on the bigger picture since he doesn’t have things like the luxury of standing around while weapons bounce off his skin or thinking at the speed of light.
The Doctor is forced to make choices that Superman never could and he is still man (or woman. Or Time Lord.) enough to face them to this day.
Superman is meant to be a Paragon of Virtue and Hope, but Superman would not be able to make the choices the Doctor has to because of his morals and that could result in the Earth’s destruction because say what you want, but Superman is not stopping a Cyberman attack and the such.
(He would not be able to get close to the Cybermen. It would only take a glance for one of the Cybermen to scan Superman’s biology and figure out how to convert him. If that happened, the world would not survive an hour.)