I'd probably give the vote to Superman, the Asteroid Feat was honestly pretty early in his career, and the Man of Steel has certainly gotten a lot stronger since then. That was back in Season 2 of the Original Show, Superman has had a season + 2 more shows to develop, at the end of the TV Series he had seemed to barely beat Darkseid (It looked like he was even struggling to hold Darkseid up at that point)
Two seasons later, their second bout goes a lot more in Supes' favor, leaving Darkseid for dead while the boy scout seems to have no lasting injuries. Now a full four seasons later with much more experience and growth (Fighting Mongul, etc), he's able to fight a much more powerful Darkseid that merged with Brainiac, with his full power seemingly only letting him beat around Darkseid for a brief moment before getting hit with the agony matrix.
Heck, we should probably skim through the series for post-Prometheus feats honestly, that Asteroid thing was so early in his career.
Anyways, Omni Man's a real tough cookie too, eating that country blast only gives him a nosebleed, but Superman has walked off big blasts too, the watchtower's nuclear beam or whatever was a nasty shot IIRC. Even if he does have the AP Advantage, I'm just not sure if he'd be able to put the Big Blue down. Superman's got a lot more going with him here, Heat Vision, Freeze Breath, though skill might be something Omni Man has more usage in, Superman's resistance to pain manipulation will keep him in the game a long while.
Omni Man's combat experience does still kind of fall short though, Superman's been able to fight against and outmaneuver Darkseid, who's had as much, if not even more experience than Nolan. I think this is a close one, but Superman's abilities, along with a great deal of resistance to pain, and his experience fighting on-par or stronger opponents could give him the win.
The closest Omni Man's seemed to fight are his own people and Invincible, but, as shown in the flashback, Viltrumite's seem to one-shot each other pretty consistently, so even that's a bit of a stretch at least compared to the all-out fights Superman has had against his superiors.
