I said look at the
curve, not just the two printed values.
That will give you a better indication of what the sub does as it moves. Xmax (and other X values)
are important to a degree. A couple mm of Xmax really doesn't allow for much volume before distortion sets in. Especially down low where the sub has to move in distances that are multiples of the higher frequencies. I forget exactly what the ratio is. Is it 4x the displacement is needed at 1/2 the octave or down 10 hz (or option 3 I'm forgetting, it's been awhile)? For a given driver we can just simplify it to position instead of displacement because the sub's cone area should be constant.
I do agree that there comes a point where more Xmax really doesn't give you anything useful because you're not fully utilizing what you have already.
Transient response (quickness) depends on the inductance of the driver.
I believe that Fs, Qts, and Vas are much more important insofar as choosing the box for a specific driver. This will help you reach the potential of the sub in the direction. It is possible to alter the quickness of the sub, its lowend extension, accuracy, and sensitivity to a degree with the box, but only up to the sub's potential. Not all subs have the same potential. Those specs do not say how accurate the sub is once it starts moving. They also don't give an indication of the transient response. They are mostly for building the box. They do give an indication of the extension of the sub, though.
I added one word to my original post and it seems to change the tone of the entire message.