you sort of have to say what time the old republic is, if this is the republic that wasted the ancient sith like Naga Sadow, then the republic would win. After all, Sadow would use the Emperor's spine for tooth floss and if he lost to the republic then so would the empire. But if this were the time of 200 years before the clone wars, then the empire. But in most cases, like the time of Revan or Exar Kun, or Sadow, then the republic.