Alright so this is conveniently something I wanted to let out for a long time somewhere.
Even without the comic as a source of anything (which shows Skeletor body Mumm-ra, then throw him a bone to body the ASOE, then let him float in his head like Firestorm)
Skeletor still absolutely manhandles Mumm-ra. Mumm-ra has accomplished more evil but is so easily and thoroughly beaten every time. For all the vastness of both his power and advantages he's a pushover. Skeletor almost wins in spite of his disadvantages. He-Man and the MASTERS of the Universe have such a military scientific and raw power advantage over Skeletor, its almost criminal. Snarf.... SNARF sandbagged Mumm-ra over such a plain open flaw. Most with intellect would never try it because most would not be dumb enough to think Mumm-ra is dumb enough to allow it to happen. Mumm-ra also got bodied by a random bounty hunter in his own backyard with relative ease. Mumm-ra gets bodied relatively easily in general. He's a joke of a villain with a lot of power and a lot of flaws.
Skeletor fights He Man and a squad so powerful, they literally call themselves the masters of the universe with no real equal until She-Ra shows up (but that's neither here nor there).
Mumm-ra, on the other hand, fights the vestiges of a extinct race. The vestiges are a literal man-child, Lion-O, a child aged into a man's body, and 5-9 servants (If you really wanna count the Ghost Jaga and Snarf, which you should because again, Snarf sandbagged Mumm-ra. I'll never let that go). And yes I say servants because they basically have to listen to Lion-O, who, being a literal man-child, for the longest time made too many near fatal mistakes). They don't have anywhere near the resources, tech, or raw power He-Man and his crew has at their disposal.
Skeletor, is significantly smarter and a better person to wield any sort of power over Mumm-ra. Almost all Skeletor's minions are trash but he has no choice in the matter. Mumm-ra has a huge disposal at with him and still loses every damn time. Sometimes his henchmen outperform him. Unreal.
But like I said, 2011 is a completely different, much better Mumm-ra who I can see giving Skeletor a decent fight. 80's Mumm-ra is a literal curbstomp. Skeletor would... well the comic basically got it right, but there are many ways ahd Skeletor could easily think of several other ways.