Since we can't count in numbers how much damage we are doing in-game, I'd say a good rule of thumb is the following.
Banshee - Drop her barriers. You don't actually have to stagger a Banshee to make her drop someone (though that works too). You simply need to knock her out of sync kill mode and into warp ball mode. Most of the time this happens the first time her barriers drop.
Praetorian - Stagger it. This can happen with enough force, but again as a general rule it will usually happen if you drop it's barriers.
Scion - Stagger it. It doesn't have an easy to read marker like dropping it's barriers, but it also has a slow sync kill and if more than one teammate is paying attention they should be a able to kill it before it completes the sync kill.
Atlas - Stagger it. You have to be fast though because it has a fast sync kill. It has a slow sync kill trigger with it's melee, so it's easier to see it coming than a lot of other sync kills as long as you're paying attention. It's a pretty fast sync kill so it's possible that an ops pack might save you if you time it right.
Brutes and Phantoms - These syncs kills are almost impossible to interrupt because they are so fast. I know a brute can be staggered out of it if you're quick enough, but you have to be REALLY quick as the sync kill is faster than most casting animations. I don't know if phantoms can be staggered out of it but I don't recall ever seeing it happen. The best way to avoid these two sync kills are to learn their triggers and avoid putting yourself in situations where it can happen. If you find yourself in such a position (phantom sneaks up behind you and staggers you with her sword) then you can try to pop an ops pack which will allow you to survive the sync kill due to the ops pack's temporary invulnerability. Ops packs don't work on Scions, Praetorians, or Banshees because their sync kill animations are longer than the ops pack invulnerability.
Edit: Since Phantoms are the only unarmored sync killers you can also interrupt it with a CC power that affects phantoms, like Stasis (or lash with proper evolution). Again though, you have to be really fast.