I have done a real-time comparison between the HDTV signals transmitted by local broadcasters in the Boston area (NBC, ABC, CBS) over broadcast ATSC and the corresponding signals transmitted over Comcast service in QAM digital cable.
The two streams were bit-for-bit identical.
I'm sure it is true for at least some and maybe most "cable-only" channels, the different providers do vary in signal quality and how much they "re-compress" the signal.
But I can tell you that for the over-the-air channels, at least in Boston on Comcast, there is no difference between getting the signal over the air and getting it from cable. The two streams were exactly the same.[*]
A rigorous comparison of "cable-only" channels would be more difficult because it's hard to get these in unencrypted form from any provider. Just counting the bitrate (if available on a set-top box) is probably a reasonable proxy, but keep in mind that some providers (like DirecTV) use H.264 (aka MPEG-4 part 10) for at least some channels. That's much more efficient than the MPEG-2 part 2 used by digital cable and broadcast HDTV channels.
[*] The MPEG-2 video elementary stream was bit-for-bit identical. I didn't examine the audio but suspect it was the same. The systems-layer framing and other streams were different, if only because Comcast's channels are at 38.8 Mbps and broadcast ATSC is 19.4 Mbps and because the program IDs were rearranged.