Hoo, yeah, you could have a lot of fun deciding what the TNG and VOY crews are like - we already know Tuvok's in the Resistance. Picard, Riker and Chakotay - what would they be like? Still skilled, but lazy or uncaring like Mirror-Sisko? And do we know if the Betazoids are "good" guys or not - Mirror Troi, anyone? If good, probably a lot more kick-ass than she is in TNG (imagine Andromeda Beka Valentine with psychic powers...). If bad, just plain scary with a decided hint of sexy dominatrix...
"That might have been the biggest mistake of my life..."
"It is unlikely. I predict there is scope for even greater mistakes in the future given your obvious talent for them."
Vila and Orac, Blake's Seven