A bigger box is almost always better.
All a smaller box gains you is less power efficiency and a higher -3db point that must then be EQ'ed with even more power.
There is no such thing as tightness.
Electromagnetic fields travel at the speed of light.
So the length of the speaker wire (and voice coil wire) has practically zero effect on the speed of the field being established or collapsing.
So what causes the cone to move, at all?
Velocity from a start of zero after time t is:
V = A * T^2
Thus how "fast" the cone moves (velocity) is proportional to the acceleration.
Newton's second law:
F = M * A
Thus A = F / M
The acceleration is proportional to the force of the electromagnetic-system.
i.e. magnet size/strength and coil size/strength. (All else being equal.)
So a beefier subwoofer would only be marginally-faster if it also didn't have a heavier cone / coil; otherwise the same speed (excluding the above reason).
The electromagnetic field traveling at the speed of light will collapse near-instantly when the music stops, so the only other force acting on the
cone would then be the air box spring and gravity (if it is an up or downfiring cone) which has nothing to do with how expensive the subwoofer is, and nothing within it's ability to control.
As you crank the power up, the electromagnetic field gets stronger, and the cone accelerates more, thus the velocity increases, the cone moves a further distance in time T.
But the amount of time T the signal is applied for remains constant, the frequency doesn't change as the power goes up, just the distance the cone travels increases.
Think about it like this:
I give you a 150lb metal box and ask you to shake it back and forth from one side of your body to the other. You won't be able to do it very fast.
Now I give you a 1lb cardboard box and ask you to do the same. You'll be able to shake it back and forth very quickly.
Your muscle power remained the same (same magnet size and coil size / strength), but the mass changed.
Conversely, if you added an inhuman amount of muscle to your arms you'd be able to "shake the heavier cone faster".
How far it can be moved in time T is proportional to your effort applied (i.e. watts), not how much muscle you have (muscle just helps you move it easier).
The physics makes sense, it's just that people don't understand it.
I guess I did put that grade 12 physics to use after all!!!