Thanks for the invitation to think about this.
I've listened to both pieces, and then tried some harpsichord versions.
Bach
Let’s start with the Bach one.
I found this Harpsichord performance which I’ll use as a reference for comparison.
He plays the first movement, in my view, with a lack of respect for its content, just as if it were a sort of game or divertimento, completely replacing the original nature of the music by a new one, it’s a bit offensive to me. Sounds like one of those pieces that Mozart plays in Amadeus. When I listen to this I think, "hey, if you don't like it, don't play it, but please, don't play around with it." And this is achieved by removing the rules of the music, the original hidden forces that constitute its value, this thin but strict equilibrium of rhythm, silence and counterpoint. The harpsichord performance is hugely transcendental, it conveys a feeling of fate as if time is something that smashes us, rather than something that we can blend, while the piano one is a strange mixture of classical leisure music and pseudo-romantic easy music, which is immaterial and quite boring in my opinion.
When I hear the beginning of the Harpsichord version, I feel the need to sit down and listen actively to what this man is telling me. It’s captivating and raises a lot of questions in my head. The piano version is just a bunch of cliches about what is beautiful one after the other and to me is no more than elevator music, something easy and banal that doesn't deserve my attention.
The difference is even more accentuated in the second movement, the andante, which in the Harpsichord is superb and fascinating, full of magnetism and mystery, transcendental. The piano version is like a light version of some Schumann youth piece. The two voices are not distinguished or contrasted but blended together, which completely removes the original quality of the piece. It’s just a bad joke in my opinion, a complete and nonsense transfiguration of the original music.
How much of this is attributable to the performer? Well, one can try to play the piano in a more dry manner, so to speak, but then one also end up with something that’s neither a harpsichord nor what the major public expects from a modern piano, so one can’t blame the performer for not trying this approach of “diminishing” the piano, so to speak. Gould more or less tries this with reasonable success, portraying effectively part of the spirit of the music. Nevertheless, I don’t think there are “good” performances of Bach on the piano, because this music isn’t for piano, as simple as that. You can have a lot of imagination and make nice music out of a Bach score with a piano, but it’s no longer baroque music, and that’s what the piece by Schiff conveys, it’s not a baroque piece, it’s something else, quite boring in my opinion.
Couperin
I’ve found this Harpsichord performance of the first song or movement.
To me it’s hard to listen to the whole piano set without having some rest. It’s too dense, partly because the use of the sustain, which with counterpoint music should be an anathema. Counterpoint assumes that notes don’t last more than written, having the sustain always half pressed all the time completely removes the silence from the music, as in the Bach one, all its air and literally suffocates it and its listeners. This music needs air, it’s built on the contrast with silence, this continuous sound which is almost a colored reverb is quite annoying in my opinion. The density of the ornaments doesn't help neither. In my opinion, they should be way much lighter and less pretentious.
The Harpsichord version of the first movement of the piece speak for itself, there is nothing more I can add to describe it in contrast to the piano one. The arpeggios, the ornaments, the silence and the tempi, the clarity, I don’t know, it’s a different music.
The same I said with respect to the Bach performance more or less applies here: the music is simply destroyed and built again with new aesthetic rules. One can like or dislike it, but, again, this is not baroque music nor Couperin, it’s something different based on the same notes, like what in modern music is called a version.
Summary
The piano performances of those pieces and many other baroque pieces are attempts to build a transcendental piece of art by means a romantic code but using music from way before, and that simply doesn’t work, is too artificial. It’s an attempt to make them sound as we, the average human, expect them to sound. To me, those attempts are sterile and what’s worse, they hide from people the true greatness of this music. People trust this guys and left the performance delighted, but I guess and hope there is in most of them a spark of doubt, the feeling that something is wrong, because it’s impossible to hide the real nature of this music, no matter how many layers of rubato, dynamics, pedal and subjectivism you put on top of it.
With the obvious differences, It reminds me when many directors don't take seriously those popular music passages of Mahler, like the 2nd movement of the 2nd symphony, displaying his ignorance by trying to convince us that they know what it's really in that music and what it means and what parts need to be accentuated in order to convey the true message it contains, completely omitting the music itself, the markings, the tempi, everything. It's like, "hey, I know what the mystery of this music is, I can decode it for you."
Of course all interpretations are legit and worth paying attention. And some or many people will prefer the piano ones over the harpsichord ones. In my view they are missing something and somehow losing their time, and I don’t think it’s just a matter of opinion, I believe it can be explained why one is better than the other, if our measure is to convey what the composer wanted to convey. My arguments may well be wrong, but I think this “rationalist” approach is valid.
I’ve tried to be clear and sincere because when I ask something to someone I expect him to tell me what he thinks.
This is in summary, with my limited English and time, my opinion.
I don't know if I’ll receive all sorts of criticism, including the classic "it's you that don’t understand those pieces", namely, stating that the author is an ignorant, which is always valid, on both sides. Well, I really don’t care as long as we talk about music. There is something that can't be changed though, no matter how bad or good my arguments may be, and it's the fact that I prefer the Harpsichord versions of all this baroque pieces, by far.
Again, thanks for asking.