Cardassians (and Klingons) seem pretty much the same in the MU as in the RU. So I doubt the mirror Dukat would be any different.
I kind of thought MU Worf was different than RU Worf.
And the mirror Garak is loads different from the RU Garak, and some of the mirror characters introduced in the TrekLit anthologies behave in vastly different ways. But the main thing, I think, is that RU Cardassians and Klingons usually act as antagonists to the main Trek cast, and, because they form a big chunk of the Alliance, are still going to be acting as antagonists to most of the "good" characters (i.e. the ones who are part of the Terran rebellion.) There's only two examples I can think of where there's a Cardassian or Klingon on the side of the rebellion (and both are from TrekLit, and one's only part-Klingon.) So the odds are that Dukat's still going to be evil.
I would tend to speculate that there was an Intendant Dukat before Kira, and that Kira assassinated him during her climb to power; I can't really see a cuddly Dukat helping the rebels in the MU - at least, not that MU. (In one of the Myriad Universe compliations, there was a good Dukat, but he exists in an alternate universe that is not the Mirror Universe from "Crossover," "Through the Looking Glass," et al.)
Note that logic does not necessarily dictate that the MU counterpart must be 180 degrees from their RU counterpart. O'Brien still likes tinkering with things, after all, mirror Odo seems to have the same need for order as RU Odo, etc.
I think we already have seen a mirror Weyoun of sorts: the defective Weyoun in "Treachery, Faith, and the Great River." We're not likely to see a real one, as the wormhole isn't open in the MU (yet). But a mirror Winn might be interesting, and I'd definitely like to see a mirror Ziyal.