The transient could be in the pass band of the filter. What I am trying to say is you have a pounding kick with a fundamental of say 45hz and it each hit is pushing the driver to say 75% of Xmax. Then the bass player plays a more nuanced note with a fundamental of around 80hz. Just for giggles let's say that that note is 9db down from the kick signal. A smaller cone could more easily be accelerated and managed by the motor to create that complex waveform. The larger driver has so much more compliance volume, shear weight and resistance for the motor to work against.
Just like a small car can more easily navigate a winding road than a tractor trailer.
Cones being fast/slow is a myth and needs to be sorted IMO.
The motor in any modern driver is more than capable of keeping control over the cone and accelerating it as fast as needed.
Here are two drivers that use pretty much the same motor, one 18" and one 21": http://bcspeakers.com/products/lf-driver/21-0/4/21sw115?impedence=4http://bcspeakers.com/products/lf-driver/18-0/4/18sw115-4?impedence=4
The difference we are talking about is more like this:
One has a moving mass of 304g, and the other has a moving mass of 335g. That's about 10% difference.
Subwoofers are like having a car being asked to accelerate to 30mph in about 30 seconds, and then smoothly decelerate. That car will not care if it has a couple of passengers that add 10% to the total weight. It's still well within the capability of the engine.
Low frequencies do not require a fast-moving cone. If the cone is moving quickly, it's producing treble and your crossover is set incorrectly.
High-frequency drivers need to be small and light. Here's an example.
A 21" driver moving 10mm one-way at 50Hz has a peak velocity (as it passes through the zero position) of just over 3m/s. The acceleration is around 1000m/s/s, so the voicecoil is exerting just over 300N of force (about 30kg, 66lb). That will result in an SPL of a smidge over 121dB at 1m, groundplane. That's around 1KW power input.
That same cone producing 121dB at 5kHz would be moving 0.01mm, with peak accelerations of 15000m/s/s, requiring 4500N of force (992lb). To produce that
force, you'll need to put around 60KW in there and hope it survives.
A 4.5" driver producing 121dB at 5kHz needs to move 0.07mm one-way, requiring a larger acceleration of 77,000m/s/s. The moving mass is about 3g, though, so you only need 231N of force to get it there. That particular driver would need around 5KW input power to manage that, which it won't survive. Dropping the moving mass further (thin titanium diaphragms) and bolting a horn on the front would improve efficiency and reduce the power requirements, though.
Edit - couple of people have posted while I typed that.
Free-air resonance is not more important than the size of the driver. Resonance (Fs), among a bunch of other parameters, will help determine the shape of the response of the driver in a given cabinet. The size and linear excursion, and thermal power handling of the driver will tell you how loud it can go.