In this case, upgrading your subwoofer is not about adding volume to the system, although that will probably also be possible. A larger subwoofer should allow you to reach lower in the frequency response range to take advantage of the LFE track on your multi-channel AV entertainment, as those tracks can get well into the infrasonic range. This is less important for music that is based on natural instruments (pipe organs notwithstanding, since they can get down to infrasonic frequencies), but if your music tastes run to music that includes synthesizers too, those lower frequency ranges that an improved subwoofer can reach can be applicable here too.
It's worth noting that while CEA-2010-A measurements for the base B&W AS610 have not been taken, nor are they comprehensive indicators of a subwoofer's performance, the ASW610XP has been measured, and its performance here is roughly analogous to the ubiquitous SVS SB-1000 Pro subwoofer. I would suggest that while the DB4S would be considered an upgrade from your current unit, there are other options to consider. Several non-B&W products might gain you equal or better performance for the same budget, particularly if you were to invest in a pair of subwoofers rather than a single larger unit. I have been particularly impressed with the output of both Monoprice's current-generation THX subwoofers and RSL's Speedwoofer 10s/12s, both of which are available at prices under $1,000. Dual subwoofers, properly placed within your listening area, can provide dramatically improved bass response within it, regardless of the volume they are set at.