If frequency response is an important element of music listening, then the LP is much ahead. The CD in comparison hits a brick wall and falls dead @ 20-22 kHz.
But there is more than frequency response in music; there is dynamics, attacks, bass punches, highs clarity, sweet mids.
After live, from personal experience, R2R tapes retain the closeness best.
And between CDs and LPs @ both 33 1/3 and 45, it's a question of the gear used and the music recording playing.
CD players are easier to setup and adjust, but other things varied, from the people who designed them and the parts they used inside and what they do to the overall sound...jitter, dither, sampling, filtering, re-sampling, processing, demodulating, compensating, pulsating, decompressing...
Turntables are the music art; they require love, adjusting, romance, care, affection and compensation.
It's funny how easily our brain is influenced. But music without fine tuning is incomplete, like many paintings that are selling unfinished but no one notices.
Only when the brush of the master has completely stopped, and the painting is installed in his frame and exposed to the gallery's wall for sale, only then when it is sold and goes in another one's room (the buyer, art collector), and that the painter has no easy access anymore to apply some final touches (some painters do, their paintings are never finished), that's the moment frozen in time in its final resting space.
It is very similar with music.
Yeah, an oscilloscope can show us that.
...That's when listening stops, and analysing starts.
By the way, in that last video above...the CD sounds much more dynamic, more full and punchy, with energy and rhythm.
The LP might have more extension in the audio spectrum, but it sounds congested, thin, lacking verve, musical strength.
That's from the video, an old inexpensive CD player, and an inexpensive turntable.
Yes, the LP is much more extended in the graph, but the sound is more alive from the CD.
So what measures better is not necessarily what sounds better. Digital is euphonic, analog is euphoric.