If you are increasing the mass by using a larger driver(ie a 15" instead of a 10') the efficiency of the driver will change, since bass is all about moving large amounts of air the larger driver will move more air(giving higher SPL) with the same excursion, but will draw more power to do so.
But with drivers of the same size but with different mass they should both move equally for the same signal BUT the heavier one will draw more current for the same output. Given the same amp, with higher volume, the heavier driver will introduce distortion before the lighter one, this is why manufactures look for the lightest material they can find as long as it doesn't compromising on rigidity.
Have a look at this
interview with Bruce Hall(President of Velodyne). He explains a number of things relating to this topic, also speaks about how the DD series are being mated with electrostatics, which doesn't surprise me as I own a DD15
.
cheers