"fast" is a totally inappropriate term to use in regards to subwoofers. The speed at which the cone moves is determined by the frequency it is reproducing, the higher the faster. If a driver can't keep up with the frequency it rolls off. Most subs break-up before they roll off. Larger drivers or multiple drivers are always better because they produce more output with shorter excursions = lower distortion.
A better term would be "dynamic" Some subs are more dynamic than others. This is very much dependent on the size of the driver and the amplifier used to drive them and the plate amps used in subwoofers generally stink not to mention a sub enclosure is not a great place for anything especially if it is a sealed sub due to temperature control. Amps working hard get hot so you can only use amplifier types that do not generate much heat. Passive subs with outboard amplifiers is a much more "dynamic" approach.