This pretty much sums off the world of loudspeaker tradeoffs. Sensitivity is affected by Fs (typically the lower the Fs the less efficient), the power handling (the higher the linear power handling the less efficient), the ultimate LF bandwidth (the lower the less efficient), motor strength (the weaker the motor for a given moving mass the less efficient), gap clearances (the greater the gap clearances the ess efficient), the VC wire profile (the steeper the wire profile ratio the better the efficiency) etc. This is why there are so many different options available to the speaker designer... to get the best mix of parameters to achieve the desired results.
Originally Posted by Arjank
Nowadays there are lot's of cabinets that sport drivers with extended xmax, lower Fs and small Vas. This not only includes longer voicecoils but also changes the design for the magnet structure, the spider and suspension. And, most of the time the cone is (a lot)heavier. All in all it takes more power to drive these kind of drivers at the same spl level as the older types.