He had few appearances, but he did give PC Superman a pretty good tussle. The trend of Supes beating Marvel via transformation exploitation started with Supes doing it to Captain Thunder.
Oh, is this the alternate Superman who could use his powers BETTER? If so, he has a GOOD chance of winning, but Captain Marvel had true invulnerability and could hardly be effected by physical attacks.
Or are you talking about the African American Captain Marvel? TOO MANY!! LOL.
Supes did seem to use his powers uncharacteristically intelligently during that big brawl him and the true Captain Marvel had, where they're both basically mind altered. Supes even busts out a "super scream".
I kind of wish the battle happened in Marvels home universe though, because the "outside his universe" weakness felt a little like a cop out.
Although, Cap still could have won with the magic lightning trick.
But yes, Supes was also pretty intelligent in the fight with Captain Thunder.. It's like the only time in his history he realizes he could use his xray vision to hide in places most people can't see in, making himself effectively invisible..
To be honest, I kind of preferred that battle over the brawl with "official" Captain Marvel.