Quick version:
Automatic Power Factor Correction (APFC) capacitor systems = step control. You add or subtract capacitance by turning fixed capacitance devices on or off. Good for small incrementqal and / or predictable changes and not much problem with inaccuracy or overshoot that will result. Other potential problem is transients causing damage to sensitive devices every time a cap bank is switched on or off.
Synchronous CONDENSER (proper term, not compensator AFAIK)= analog control, i.e. PF is altered in direct proportion to what is needed without overshoot and with a high degree of accuracy. Can accomodate a wide swing of operation at any time, and creates no switching transients (except when motor is first turned on. There is even a case to be made for the SC being used to reduce harmonics. Drawbacks are power consumption of synchronous motor if not being used for some other purpose, and initial cost if one does not already exist, although a good engineer can probably make a case for payback.
Quick and dirty rule-of-thumb,
500kVAR and under, Capacitors
Over 500 - 1000kVAR, consider SC,
Over 1000kVAR, SC for sure
6kV system may warrant SC since APFC capacitor systems are more expensive in MV, but then again, so is everything else.
Try searching for info on synchronous condensers. People that can supply them usually will supply APFC systems as well, but not vice-versa. Quando Omni Flunkus Moritati