it's hard to say, really. i mean was he directly responsible for the burning of the library in the dreaming? that would mean multiversal scope (no surprise there) if we attribute that to him. we know in his aspect as the dragon, he had the power to destroy worlds (READ: universes) that were considered failures, and that the forger, whom he killed, had the power to create universes, some of which took shape in the positive mulitverse. he was mentioned as part of the trinity that also included the monitor and AM, so that's another indication. he is at least on par with them, but there was also a scene (with morrison's map) that indicated the DM was far and away larger than the positive matter multiverse.
https://imgur.com/a/gWqIg
that would seem to imply his power>monitor or AM, since they were exact equals. so maybe in the DM his power IS greater than even what they could reach? i could never figure out if this scene was intended to show intellectron fleeing from the carrier, or chasing the thule:
https://imgur.com/a/R7hSO
if one of the gentry is running from barbatos' power, that is a pretty impressive feat as well, but seemed pretty ambiguous. i dunno. we had loads of hype, but not a ton of substance it felt like. i'd wager that very few could walk into the DM and defeat him, but take him out of the DM and he seems....very much less.