Let's look at two generic examples using the CEA-2010 industry standard measurement protocol.. Subwoofer *A* has a maximum output capability of 105dB at all measured frequencies----20,25,31,40,50,63hz. Subwoofer *B* has maximum output capabilities of 105dB at 20hz, 106dB at 25hz, 107dB at 31hz, and 110dB at 40hz, 50hz, and 63hz. Now, before we go further it is important to remember that at 105dB, subwoofer *B* will very likely maintain all of its inherent frequency response "linearity". So if the source material only requires 105dB of output....both subwoofers will sound very much alike. This assumes all other performance characteristics(group delay, impulse response, stored ringing, overall frequency response,etc) of the two example subwoofer are very similar too of course. For this example, let's assume these variables are all similar though so we can focus on one variable at a time.
Now, what if the source material requires the subwoofer to reproduce bass louder than 105dB at the seating position? What about 110dB? Well, subwoofer *A* will not provide ANY of this additional material that you are intended to hear and feel. All of the dyanmic headroom is "squashed" and the audio presentation will suffer accordingly. On the other hand, subwoofer *B* WILL provide all of this material in the 40hz and up range AND a good portion of it in the 25-40hz range. Will you experience all of the intended bass effects at the 110dB level from subwoofer B? No. But you will experience significantly more content that you are absolutely intended to hear/feel. The whole idea with audio reproduction is for the system to have the ability to reproduce AS MUCH of source material as possible.