Pfft, Asmodem and Demilame are both posers. One imitates a real world evil who always gets the short end of the stick, and the other's name is gorgon with a lame suffix. Magic wands and tentacles can't compete with real power...
The Lady of Pain would annihilate them both. With all of their armies. At the same time.
See, it's gotta be Demogorgon: he's got tentacles. We all know that the tentacular beings out there can distribute some advanced clobbering: just take a look at Cthulhu, or Shub-Niggurath or mind flayers.
Tentacles rule the lower planes!
That and he has baboon heads. Baboons are way nastier than goats or debonair sophisticates.
Yeah, (going by 1e) demon princes and arch-devils are classed as Lesser Powers. 1e Deities & Demigods has Cthulhu, Azathoth, Cthugha, Hastur, and Yog-Sothoth as greater gods, with Nyarlathotep and Shub-Niggurath as lesser gods and Ithaqua as a demigod. So in 1e, maybe a wash?
If you go by the Call of Cthulhu RPG Cthulhu and Hastur are just Great Old Ones, essentially demigods, whereas Azathoth, Nyarlathotep, Shub-Niggurath, and Yog-Sothoth are actual Outer Gods. Call of Cthulhu d20, which is much more similar to 3rd ed, more or less concurs, having Azathoth as a greater god, Nyarlathotep, Shub-Niggurath, and Yog-Sothoth as an intermediate gods, and Cthulhu and Hastur (as well as Chaugnar Faugn, Cthugha, Dagon and Hydra, Eihort, Glaaki, Ithaqua, Mordiggian, Shudde M'ell, Tsathoggua, and Yig) as demigods. So...maybe advantage Shub-Niggurath?
The way they're usually described I'd actually expect Shub-Niggurath to lash out with tentacles and random spells against anything in sight before disappearing if bored or actually threatened. The Cthulhu Mythos gods generally consider humanity beneath their notice, but how they'd react to a genuinely superhuman threat like a demon prince or arch-devil is anyone's guess.