I have actually owned both the DD-10, 12, and REL Storm III. Everything said above is true about the advantages of Velodyne because of their superior technology (& flexibility to the nth degree). That said, a few observations for anyone looking at buying these three
1) Between the two Velodynes, the 10 inch is all you need if you don't have a huge room or listen to organ music (see notes below if you're interested in why).
2) Between Velodyne and REL in general, what the Velodyne gives you is peace of mind because you can see (instead of just hear) on your TV what the sub is doing graphically (and allow you to make it nearly perfect easily), and also the servo technology makes it so fast and accurate (less distortion). It will produce the notes faithfully and you can see as well as hear it. Once you've done that, you feel like you know you have the best and don't need to go shopping anymore, which ultimately makes you sit back and enjoy the music.
3) All that said, don't discount REL. If properly set up per their instructions, they are wonderfully musical subwoofers - let's face it, science tells us that small levels of distortion at lowest frequencies is nearly inaudible - I might even guess that some of this distortion is what makes the REL sound so good ! Make no mistake though, the REL blows away most other 'box' subwoofers, even the cheaper Velodynes. What am I getting at? Well, you could argue that if you find two Strata's or Storms used for a good price (less than a Velodyne), the stereo pair when set up right might be a great thing.
4) Last, if you listen mainly to music that doesn't go much below 40 Hz, either sub is fine, and the REL might even be better, because all of their posturing about "loading the room" really seems to work well. It gives you the spatial clues that only bass information can provide. Again, if you listen to organ music (or other music with one note pitches at 16-32 Hz), the Velodyne will please you most.
I needed the '12' -- I have recordings that required the larger model - like one (Raven Records; Holst Planets) where the organist plays 5ths in the pedals (like the tympany in the original score, I believe on Saturn). As organists/audio nerds know, playing 5ths creates harmonics an octave below (known as "resultants" on the organ registration), and in this recording the organist is already using 32 foot pipes here (so technically you're getting pitches that 64' pipes would create). Anyway, it sounded like the 10 inch was regulated enough to not "blow" (bring in images of Scotty here from original Star Trek), but simply could not move enough air to make it sound realistic. It sounded strained. The 12 inch (do the math on the surface area between the two drivers!) did it just fine... love to hear the 15 or 18...