He's pretty dam bad ass, in the Alan Moore story involving Mongul. I've been told that only Pre Crisis Validus and Darksied to could match him physically.
Yeah. Pre-Crisis Mongul was casually standing up against the entire Legion of Superheroes.
He was virtually unaffected by Hal Jordan (GL) and Supergirl combined.
He thoroughly defeated Superman - physically - when he faced off against him WITH Starman.
One time Superman did beat him, by going all out with speed and strength and heat vision...and fell into unconsciousness right after that.
In "For the Man Who has Everything", it was Superman's speed and heat vision that hurt Mongul more than his strength. Yes, Superman almost killed him, but then again Mongul almost killed him as well.
He also casually tossed around Pre-Crisis Wonder Woman (with Kryptonian weapons) in that same arc.
Wonder Woman couldn't even hurt him. Moore's Superman's stories are really good, I love the Superman For all seasons. I think Mongul could do with some more respect nowadays. I think him and his family and maybe War world could do with a specific origin. I once heard that War World, was actually a future version of Earth that was transported back in time.
He did pretty well against the whole Trinity at the beginning of the Crisis. Mind you i don't like the idea of Hal easily piercing his skin with arrows. Especially when you consider the previous scans involving the apparent strongest metal in the universe.