Right, let's get into this.
AP/Durability: Thor scales around 337 Megatons, while Superman scales a fair notion above 177 (Shazam was overwhelmed by multiple Paradooms and seemingly killed; he was also gored by them whereas Superman took on dozens of them with only scratches and lacerations. Also physically overpowered Darkseid on his own, Shazam needed the league.) It's either negligible or slightly in eithers favor, though I'd bet on Superman being physically stronger.
Lifting Strength: Massive advantage for Superman, could pretty much restrain Thor one-handed. Which is important because Superman's a grappler when he's not punching or shooting heat vision; he does it a lot.
Abilities: Thor's got more up his sleeve, though seemingly isn't Magic so Supes doesn't have to worry about getting hit. I'm not sure if Thor's the type to BFR because he's usually an honorable fighter but he could do that as a win-con if things get tough, and Stormbreaker's (or Mjolnir whichever one it is) gonna be rather annoying to dodge around.
Skill: Probably goes to Thor, but Superman's no slacker in this area. He was able to fend off Wonder Woman, and overpower Darkseid; whose managed to overpower the rest of the Justice League before, they needing to take out his eyes to start dishing out real damage. Even then they were still getting beat around until Clark showed up. I don't how a lot about Ultimate Marvel, but I'll just say neither has a glaring advantage.
Verdict: This is a pretty good match up, Superman and Thor pretty much match each other blow for blow here. AP is likely negligible, Thor's got the edge in versatility and Superman's got that absurd Lifting Strength advantage. I don't know their stamina but I'll assume both can last until other drops from wounds either than exhaustion. Skill-gap is probably nothing great for either of them. But despite it all, I'm gonna have to side with Superman, as he's got the most glaring advantage here; that being his absurd LS advantage. Superman's got so much more on Thor it's not even really all that fair, especially if Mjolnir/Stormbreaker starts to get annoying. A good grip and Superman can put this on his terms.
Interesting match-up, but 6/10 I'm going for Supes.