the "cleaner/musical" qualities are very subjective, and in this level of subwoofers, we've seen both eD and Epik subs deliver "musical" performance at the highest levels.
from a Physics standpoint, it is much easier to predict how each will behave. Both are 18" ported subs, in relatively big enclosures and similar power plants. The big difference is, of course, the driver.
the Conquest is using one of the most high powered 18" drivers out there, with mid to high 30's mm Xmax, 75mm peak to peak, 70+ lbs behemoth with a triple stack magnet that is over 9" in Diameter
alone. It is rated to very high power ratings, and of course, those who have used Chad's drivers in the past (ie, Avalanche, havoc, etc) know about their accuracy and transparency.
the eD is using this driver if I'm not mistaken (someone please correct me if this is not the case):http://www.edesignaudio.com/edv2/pro...products_id=37
It has 22mm Xmax, an Fs of 26Hz, a Qts of .369, and has a pretty small motor in comparison.
I would have to think that unless something is drastically wrong, the Conquest should deliver substantially higher output and deeper extension, while maintaining as musical (if not more) a quality, subjectively speaking of course. Of course, the eD is cheaper as mentioned.