The Vong are finally in a setting where they actually appear to belong. Great fun was had by all.
Fire-power being roughly equalised (which makes reasonable sense), the Vong would seem to have the decisive advantage over the Imperium. The Vong are demonstrably capable of taking on the bulk of a whole galaxy, in a scenario where their enemy has safe and reliable access to incredibly powerful FTL (as in: can cross the entire galaxy in under two weeks, and fast ships can do it in days). In this scenario, they face off against a power that only controls a segment of the galaxy, and access to FTL is inherently dangerous.
The Imperium is far more militarised, of course, being pretty much at war with everyone since always, but they're still a "regional" power (when considered on a galactic scale). If it's purely Imperium-versus-Vong, I think the Imperium is pretty screwed. Although it's going to be an enormously horrible war, and after the Vong win, they'll be so exhausted and ravaged that the other 40K powers just gradually cut them to pieces anyway.
If the Vong just invade and start waging war against everybody for religious reasons, they're completely screwed, because everybody in 40K is all about the constant war, so if you pivk a fight with all of them, you'll get slaughtered. (And then they go all back to killing each other.)
Interestingly, I think Chaos is not that big of a danger to the Vong, since I think it's a safe bet to assume that by the same rules that cut them off from the Force, they'd also be cut off from the Immaterium. The big threat to the Vong, I think, would be the Tyranids. To them, the Vong with their bio-tech would be a giant feast. They'd consume all they could, and absord any useful genetics and bio-tech while they're at it. (Which would, horrifyingly, make the Tyranids more dangerous and terrifying.)
...An exception to this would be if Onimi in particular gets corrupted by Chaos. He'd admittedly be a prime candidate for it. Chaos wouldn't be able to ensnare the Vong, but they'd be able to ensnare Onimi, and thus still exert control over the Vong...