I don't know about the specifics of characterizing beam-pattern, etc. I am pretty sure, Kinect 1.0 can be more directional in spite of having fewer microphones because the microphones are cardioid, as opposed to the uni/omni-directional ones used in the Echo. Also, some parts of the design of the Kinect speech processing pipeline is public. You can read about in Ivan Tashev's (of MSR) book [1], IEEE Signal Processing Magazine article [2], and some presentation videos he has online [3]. Also, see his publication list, a lot of papers are relevant to the Kinect speech pipeline http://research.microsoft.com/en-us/people/ivantash/publicat...

Also obligatory, why the downvotes?

[1] http://research.microsoft.com/apps/pubs/default.aspx?id=1022... [2] http://research.microsoft.com/apps/pubs/default.aspx?id=2012... [3] https://www.google.com/search?q=tashev+video+lectures&oq=tas...