The Vong would crush the early Sith empires, too much number and power.
The Galactic Republic and Sith Empire circa TOR... are a lot bigger, but still not as big as things will become, and their ships aren't as strong as later ones. Lots of Jedi/Sith warriors would help, but... I'd say probably the Vong. Best-case, only one of them falls, worst, both do.
PT Galactic Republic and Confederacy of Independent Systems. Depends on how quickly they can militarize, but the galaxy is big and the production of the galaxy ramping up. They'll stop the Vong, quite possibly even faster than the slow response of the Vong war did, though with many many casualties and plenty of planets lost.
The Galactic Federation of Free Alliances circa Dark Nest. Well, the GFFA will respond fast, but they're already hurting from all the damage caused by... the Vong War, which they haven't near recovered from. Another Vong war so soon would be devastating. They *might* be able to pull it out but it'd be incredibly hard and a close thing, they could easily lose, or at the least be broken even in victory.
The Galactic Empire at its height. They win, being unified and pretty militarized with strong ships. The Vong can't take a fairly healthy unified galaxy, similar to the PT/CIS scenario.
United galaxy, Legacy era. Here, unlike Dark Nest they've had a chance to recover from the first Vong War, and unlike the others they also have a lot of knowledge of how Vong fight. Their ships are better than the GE or PT ones, they've got multiple big force orders. The damage caused by their own wars hurts some, but overall I expect them to do the best out of any of them.