In "The Man Who Has Everything", wasn't Superman mad enough to kill Mongul? Mongul was still able to take what Superman was dishing out, and if not for Robin's interference, wasn't Mongul about to win their battle?
That's a lot of what I actually liked about Mongul. Jim Starlin had introduced a new character into the Superman mythos who was so tough that Superman's superior speed and other abilities hardly mattered to him. Sure, Superman could hurt Mongul, and Mongul would certainly know he was in a fight, but it made their battles all the more exciting! The reader never knew for certain that Superman would actually be able to beat that monster.
In the DCCP team-up with Starman, Mongul was still able to fight, but for his own cowardice. Superman even admitted how glad he was that that was true to Starman, due to his own tiredness.
I know only of a few appearances Mongul made against Superman Pre-Crisis: the 3-parter with Martian Manhunter, Supergirl, and Spectre, the afore-mentioned team-up with Starman, and "The Man Who Has Everything." I can't recall if Mongul was in The DC Challenge, but were there any other appearances?