It seems to vary greatly by institution. At mine, for example, they don't even do c-sections. They don't do any deliveries actually; it is purely a consultation service and the patients are referred back to their general ob for delivery. The only operative procedures I've seen them do are cerclages. They do, however, do many office procedures: amnio, CVS, and multiple pregnancy fetal reductions. And they do extensive genetic counselling. And scanning. Lots and lots of scanning.
In talking with one of our MFM docs, it seems like perinatologists run the gamut from being general obstetricians with an emphasis on high risk, to scan jockeys who only do ultrasounds, and everything in between.