What are the sonic differences between…

My point was, if the subwoofer didn't make an audible sound and just put out the waves, how would you know which one was better? It would make a difference in that the less distorted waves would be the better of the two, but I didn't know if that could be easily determined.

The answer is that the waves are quite audible. The differences in subs are audible as well and can range from subtle (when comparing very good ones) to immense (when comparing for a example a good one to a boomy home theater one).

Okay Up-since you refuse to provide the application and you don't like "it depends", here's my next best answer. Ideally, all subs should work the same, with the only difference being how much they load any given room. Having said that, I would choose the Velo 18 because it would never strain for impact. Connections can be another difference, as some don't provide speaker level options. I own four different subs, two for HT LFE (separate systems), one for HT center channel extension (speaker level) and one in 2-channel vinyl-based system. I can hear and feel each sub in its application but cannot identify sub location.

One more thing, I used to own a Velodyne and really liked the quick, tight, deep punch in HT application.

I understand why you wanted to keep this general, but can you at least say whether the sub will be used in a HT, music only, or some mix thereof? Might help surface some useful information on one or both of the subs you're looking at, or maybe introduce some other potential options. Just a thought, and best of luck in your search.