Variable frequency drive

It's simpler and less controllable.

Induction motor is cheaper and needs less maintenance.

Large Synchronous motors (of the type that would use an LCI drive) are often used in large facilities to run in a leading power factor mode in order to correct for lagging power factor of other induction motors.

Synchronous motors tend to turn at slower speeds, so if the application is for extremely slow speeds, a large synchronous motor will often be physically smaller than an induction motor with many many poles.