Starburst is the way Moya itself travels through space (as an emergency escape technique) while it usually travels through space at FTL levels on its own natural ability. It was a plot device used to explain how Moya could evade the Peacekeeper Command Carrier and not be tracked.
Ships in Farscape usually travel using "Hetch drive".
Hetch drives are extremely slow by FTL standards (with "hetch" just being a measurement of speed); basically just a faster form of Star Trek's thrusters. It takes weeks if not months to travel between neighboring stars using them. Starburst is pretty much a "jump drive," while other ships used something closer to a warp drive. They travel in normal space, Moya hops a ride through bordering dimensions. Hell, even using the slingshot technique Crichton came up with during the premiere was significantly faster than what a hetch drive could do.
Again, the big deal about Starburst is that it's unpredictible and impossible to track. But if a Leviathan has some form of tracking device onboard (as Moya did several times), a Peacekeeper command carrier could easily catch up with it. Considering how close the calls were on several occasions, their form of travel is just a little faster than what a Leviathan can do by Starbursting (considering they need some downtime before they can make another jump). My guess is that the Peacekeeper's FTL method required an acceleration phase. They can't just "jump" to max speed. That would explain a lot, such as why they couldn't chase Moya during the aforementioned slingshot in the premiere.
Also keep in mind that Crichton had a hetch drive installed onto his module, and despite having one he was all but stranded when Moya Starburst away at the end of the third season.