Here at Viciedo Web Development, in the last few years, we've encountered this question many times and the answers is of course; it depends on your situation!  Adaptive design is specifically designed for touch interface phones and overall is the better solution but responsive design is cheaper so it has it's place as well.

Give us a call 406-570-9189 to get the right solution for your mobile web needs.

Also of importance is I've been seeing a few mobile apps come out here locally that really don't offer much different than an adaptive design would.  Here's an interesting article for more information:

"it's getting easier and easier to create rich touch screen user experiences with the browser without having to create platform-specific apps." 

http://readwrite.com/2010/02/02/mobile_app_or_browser-based_site