Everything has pointed to the Vasari's enemy being something of their own creation. The opening video begins with a Vasari research base before describing their exodus, and most accounts indicate that whatever it is, they made it.
Replicators. *cough, cough*
Seriously, though. Stargate and SoaSE are very similar:
TEC = Humans (obviously)
Vasari = Goa'uld
Advent = Ori
Mystery race chasing the vasari = Replicators
And if there was a race who was an enemy of them, as suggested above, they'd be the Asgard.