They're two very different products. The Response are basically little 'pillows', absorbtive on one side and reflective on the other. They're soft and flexible, designed to be mounted with pins. I can say screw WAF since I live alone, so I just stapled mine up.
The Adapt are rigid boards, reflective on the front with fiberglass behind. They're fully wrapped in fabric and look very, very sharp. They attach with an ingenius hidden spring-and-loop system that's so simple that it's a wonder everyone doesn't use it. The install is very neat & clean. Since my listening room does double duty as my HT room, I chose black to help darken the room but if you get the white ones they'd be very unobtrusive.
The Adapt are more advanced and more effective, although considerably more expensive. While they do a great job, I wouldn't recommend them to solve bad bass problems- in my experience they help with bass but are more effective from the lower mids on up. But to be fair, I haven't tried using 10 or so Adapts; mine is a mixture of the two. Nathan claims an Adapt system with enough peices for your room will do deep bass. I have no reason to doubt his as his stuff does what he says it does, but I can't confirm it, either.
The Adapts are slicker looking, more professional in appearance. The Response's look a little DIY/homemade. I think your WAF will be much better with the Adapts. I suspect they could even be painted or dyed to better match your walls if your room has some unique color.
