Just to further clarify, the piano track(s) you hear between the two mixes is actually different.From This Moment On was originally cut from the Music, Music, Music special, so the video and mono audio together has never been released.
The U.K. CD version of Interpretations from 1994 (the CD that has 21 tracks) features the original mono mix, whereas the US CD (with 16 tracks) has the remixed stereo version that's found on the DVD. Of course, Richard always recorded and mixed the Carpenters TV tracks in stereo, with just the final mixdown for TV being in mono. And that's really the difference in the two: in one the piano's in mono, the other the piano is spread across the stereo stage.
The original was cut mono in 1980, and can be heard as you mention on the '94 UK release of this compilation. For the '95 US release, Richard actually re-played the entire thing so that it could be not only mixed in stereo, but also given a little more "spunk" than the original performance.
Not too long after he did that session, engineer Bill Smith (who was then a second man at Capitol and part of the project with Richard) was working with me on a project over at A&M. He recalled how blown away he was at Richard's some-odd "30 or so takes" he did in order to nail it, as there was no click track in which to reference - only Karen's voice! To quote Bill, "Richard was a MONSTER on that piano!"