Really wish Doc had some competent competition in the Watchmen-Verse for a good guage of his power level. Best one could estimate is that he's a Captain Atom analogue of unknown degree, and Captain Atom could put up a valiant effort against Thor, though would likely lose a majority due to Mjolnir.
I say non fight due to the lack of evidence on Doctor Manhattan's part, but Manhattan's too good of a character to simply arbitrarily check off as losing to Thor. He lacks any credible offensive feats pointing to his being able to win. He's like Surfer with zero combat feats whatsoever.