The differences are significant:
1) The Microsoft app works in real-time on the phone, rather than 123D Catch processing in the cloud
2) The Microsoft app shows real-time results, so you can see where there are issues, and continue to photograph until they are resolved. With 123D Catch you patch errors in post.
3) The Autodesk 123D Catch app actually exists, and the earlier web-based version has been around for about four years.
I'm kind of surprised that Microsoft isn't using the acceleration and magnetic sensors in the phone to help determine the camera position. It's one of the features that phone cameras have that DSLR's don't.