Aaron L said:
Azathoth, Shub-Niggurath, and Yog-Sothoth, on the other hand, are personifications of universal principles, and are of a whole other level of power.
The Lovecraftian trio there are probably closer in concept to DnD Archfiends rather than DnD deities. Cyric and Nerull might have an evil alignment, but Mydianchlarus and Demogordon etc -are- evil. DnD gods are largely the embodiments of their worshipper's beliefs taken form, while the archfiends tend to be the raw embodiments of that alignment personified.
Deities can be forgotten or their worshippers can die off, leaving them a petrified lump of stone in the Astral. So long as their alignment exists, archfiends don't have that issue to worry about. They're made of baser stuff. Being a true deity has its perks, such as not being tied down in your power to a plane or layer of a plane, but also carries responsibilities and risks.
In giving stats to archfiends it's certainly an enigma that you're faced with:
1) some people want to fight them at the end of a campaign, somewhere in the 20ish level range.
2) Then you've got precident of archfiends killing deities: Asmodeus rumored to have killed Abriymoch, Yugoloths having made Khin-Oin from the spine of a deity they killed, Levistus winning a protracted war against Set and Sekolah both, and the fiends (likely the yugoloths) having put a definative end to deific involvement in the Blood War by killing one nameless deity of chaos and somehow affecting every other deity involved till they all withdrew and have stayed so since that point. In DnD in most all examples the fiends are treated with kid gloves by deities, outside of rare gambles when a deity manages to kill an archfiend and pacify its kindred to avoid being curb stomped by an infinite plane of them. Deities don't interfere with the internal politics of the fiends out of actual concern, not just because it's beneath them or something contrived like that.
3) Some folks want them with stats but on the order of deities (who they also want statted)
4) Some folks want them with no stats
So somehow you have to remain true to the history of the Archfiends in DnD while somehow making one or more of the trio of perhaps mutually exclusive camps happy. Won't be easy. You have to have archfiends that can, on their own power and influence, hold infinite planes or layers of infinite planes from true deities and are viewed as largely seperate but equal powers.
A deity is nigh all powerful within their discrete domain, but outside that domain, they recognize that the fiends native there and their rulers are in control. A deity is nigh all powerful in their own discrete domain but Mydianchlarus and the layer of Oinos might as well be the same being, same thing with Demogorgon and his layer of the Abyss, or Levistus with Stygia. On the other hand that deity will have its own general (ie not within its domain) deific power anywhere, while those archfiends might have considerably less outside of their plane.
How to put that into game stats? Especially given the unfortunate precident that we have to go along with for with deity and archfiend stats in 3e? It won't be easy to reconcile those with the archfiends' history in the game, plus some folks want to use them as targets.