BASICALLY, it works like this. Assuming everything is the same ecxcept for varying the volume of the box a SMALLER box will play LOUDER but not as LOW ("monster bass") and a BIGGER box will play LOWER but not as LOUD ("audiophile bass"). "Normal" bass is a compromise of the two and somwhere in the middle.
Cone movement will be less w/ a smaller box but this is immaterial if the driver is operating w/in it's designed limits. The smaller box will be able to handle more power (excursion or movement wise) than a larger box due to it's "tighter spring" as SSQATCH put it. Contrary to what a lot of people assume, monster bass really isn't that low. The bass you feel that punches you in the chest is around approx. 60 Hz which isn't all that low, especially in a car. If you center output in that region w/ the smaller box you will get louder bass, if you add the extra power that this type of box affords you will add to that gain.
To put it in gearhead terms, the enclosure is like a camshaft that determines where the output of the system happens. Like a camshaft you have to decide how you want the curve to look, if you want a lot of high RPM power (loudness) you will have to sacrifice some low RPM torque (low bass).
Finally, JL builds excellent speakers and their reccomendations for their use are accurate for the reasons I mentioned above. Soundwaves do not bounce around in subwoofer enclosures. The wavelengths of sub frequencies are much longer than the enclosures used to contain them, longer than our big ass cars for the most part as well. The subs cone will only work to perssurize and depressurize the enclosure. Higher frequency drivers/enclosures are another matter and will bounce around, to use simple terms.