CD v.s LP - When comming from the same MASTER

Metralla....To represent a time-domain waveform by Fourier coefficients, the waveform must be periodic, and remain of fixed spectral content (at least during the time interval of the FFT). Music isn't like that. There are momentary wavefronts with steepness equal to that of a sine wave at well over the 20 KHz upper frequency of human hearing.

Pabelson and others...Summing of the bass (like the drastic RIAA equalization) is a topic that vinyl fans like to ignore. I believe that the reason for suming is to enable non-audiophile phono pickups to stay in the groove. Large vertical groove modulation would raise havoc with VTF, and even cause the stylus to hop out of the groove. I think that the summing is rather gradual in slope, but begins around 200 Hz. Whether this is a problem or not is another thread. Many people sum the bass to a single subwoofer. (Not me).

Horizontal groove modulation is what needs to be limited so as to save space on the vinyl. This is done, first by the RIAA equalization, and secondly by variable groove spacing (according to the momentary LF signal content).

An afterthought...Some of the very first stereo LPs, Audio Fidelity "Dukes of Dixieland" did not sum the bass, at least that I can detect on my system. Some of the very first stereo recordings (Vanguard in particular) also stuck with two microphones, and that also was better than early attempts at multitrack recording. Sometimes progress goes the wrong way.

Twl...You make sense. Mostly.
The Nyquist criteria calls for sampling to be at twice the highest frequency of interest: if this is true the analog waveform is represented without error. BUT...Nyquist was talking about sine waves. Music is not a sine wave. That's why the CD sampling frequency of 44.1 KHz is not adequite. In my experience (non audio) sampling at about four times the highest frequency of interest was useful. (Higher a waste of time).

Analog recordings TRY to reproduce the signal in a continuous manner, but HF filtering gets in the way. A LP can be "read out" with an optical microscope instead of a phono pickup. A few exceptional recordings have groove modulations up to 22 KHz. If the wiggles are not in the vinyl you can't say that the audio system responds.

"Better", or "different"? That there are differences cannot be argued. Of course the two products were mixed down differently, perhaps even by different people. For the LP there must be RIAA equalization and blending of the LF material to mono (to avoid vertical groove modulation) and in most cases there will be peak limiting and compression so that the softer passages are out of the noise floor. (Remember, Albert, that not all people have $75,000 turntable systems that miraculously remove surface noise, and they buy most of the LPs).

So I conclude that there will be differences, and some will prefer the LP version.