In any installation, generally the sub with more displacement will be louder at most frequencies.
However, the subwoofer that is stronger that has an equivalent Sd will have the potential to be louder in a narrow frequency band, than an otherwise similar sub that has more displacement (excursion) capability.
In an SPL competition scenario (which are the numbers you seem to be referencing... "metered" systems //content.invisioncic.com/y282845/emoticons/wink.gif.608e3ea05f1a9f98611af0861652f8fb.gif), the sub is in a box that's tuned to a frequency adjacent to the car's natural interior resonance, and the only thing being played is a "burp" of that particular frequency.
This "superior dB level" SPL sub will get it's ass handed to it - in terms of dB - as soon as you play frequencies that aren't in the SPL sub's narrow range, by the sub that has more displacement...
Even though the higher displacement sub couldn't ever put up the peak SPL number of the SPL sub.
Oh... and did I mention, that typically the trade off IS in peak strength, vs a motor that trades the high peak value to maintain it's strength across a greater excursion range?
So...
Which sub is REALLY louder? //content.invisioncic.com/y282845/emoticons/biggrin.gif.d71a5d36fcbab170f2364c9f2e3946cb.gif