Faster-than-light drives use element zero cores to reduce the mass of a ship, allowing higher rates of acceleration. This effectively raises the speed of light within the mass effect field, allowing high speed travel with negligible relativistic time dilation1 effects.
Starships still require conventional thrusters (chemical rockets, commercial fusion torch, economy ion engine, or military antiproton drive) in addition to the FTL drive core. With only a core, a ship has no motive power.
The amount of element zero and power required for a drive increases exponentially to the mass being moved and the degree it is being lightened. Very massive ships or very high speeds are prohibitively expensive.
If the field collapses while the ship is moving at faster-than-light speeds, the effects are catastrophic. The ship is snapped back to sublight velocity, the enormous excess energy shed in the form of lethal Cherenkov radiation.