Doesn't the fast/slow thing have more to do with overshoot and ringing? (treinage -in French)
A woofer cone that doesn't start - and especially stop - with the waveform is one that sounds slow.
Could be for whatever reason, even the box.
Most pro woofers have strong motors and stiff cones and suspensions. They tend to sound "fast" because they don't flop around much. Put them on an open baffle and it can be very surprising!
At least, that's what I hear and how I understand it.