Personally I don't care what he is "officially." I was thinking about the hierarchy of hell the other day and I think I'm going with something like this:
Duke of Hell: Ascended Initiate (=demigod)
Archduke of Hell: Ascended Temporal (=lesser deity)
King of Hell (one of the Nine): Ascended Celestial (=intermediate deity)
Emperor of Hell: Ascended Empyreal (= greater deity):
So Asmodeus is equivalent to an intermediate or greater deity in my book (depending in which fiction you choose to believe)
Well that probably works, as long as you give a thought for how one thing impacts everything else.
(IMO) I don't think there is a valid reason why Asmodeus should be more powerful than say Orcus, Demogorgon or Graz'zt.
In the AD&D lore at least, Asmodeus position as King of Hell was tenuous and held together like a house of cards. Once you start just boosting him 'because he's the King' you lose the whole political aspect that makes the Nine Hells so interesting and ripe for roleplaying. Having all the Archdukes (including Asmodeus) be Lesser Powers is maybe more fun.
However, the fly in the ointment was 2nd Edition's introduction of the Intermediate Deity status. Which was probably used to differentiate between the Greater Gods who were
not the heads of Pantheons from the Greater Gods that
were the heads of Pantheons. But that nuance seemed lost on everyone (including the designers).
Interestingly it all made sense in AD&D where the demons, devils and daemons were accredited with one Greater God and then the Archdukes and Demon Princes etc. For the Devils that Greater God was the imprisoned Lucifer (via the Dragon Magazine article) which played into the Dante's Inferno aspect of things.
So I don't think there is a right or wrong way (especially given how few campaigns it will be relevant to) but I would lean towards making the Archdukes all Lesser Powers in 5E.
It would be nice to see an Archdevil, a Demon Prince, a Daemon Master, a Slaad Lord, an Elemental Prince, an Elder Evil and a Primordial (with a bunch of attendant servants) in the 2025 Monster Manual given they have stated they want to flesh out the higher Challenge Ratings a bit, but I suspect that is but a pipe dream.