The only way LPs can hypothetically be better is high frequency response, but that is above the range of normal human hearing anyway.
That also assumes they are played on absolutely perfect equipment (which which rules out anything any normal person can afford anyway).
In every other way - noise, low frequency response, durability etc. CD is better regardless of equipment used to play a vinyl disc; it's simply superseded by better technology.
Newer digital audio formats with higher sample rates and higher bit depths are better still, 2 - 8x better resolution than CD, and are far beyond any "vinyl" record system.
[Electronics designer and audio enthusiast for 40+ years].
Edit re.comments to this and other answers:
And any generic CD player, PC audio setup or "surround sound DVD/Blu-ray player" will have better audio quality than anything less than any "vinyl player" being pushed on the public..
How does my answer not fit with the "middling or less" quality gear?
..then perhaps in time you can hear the better sound quality...
The "better sound quality which only possibly (hypothetically could only) exists above around 20KHz ??
Exactly what percentage of adults old enough to appreciate serious music can hear that range?
Near enough zero. Sorry, but you make a meaningless claim there.
The best _possible_ noise floor for LPs is around -60db to just possibly -70db. That is a limit of the physics of the mechanical reproduction system.
The 16 bit digital format used in CD audio has a fundamental noise floor of about -100db.
Any distortion caused by digitisation within normal audible frequencies is far, far below the levels that any "vinyl" system can possibly reproduce undistorted on any possible equipment.
LPs (vinyl) are simply NOT, EVER as good as CDs on a technical basis.
Different recordings may be different qualities and different producers may mix masters in different ways, so subjectively different releases may occasionally sound different, but that is nothing to do with which user format is technically better.
Re. the "top technology" - Blu-ray audio can be anything up to 24 bit 192KHz sample rate. I suspect quite a decent percentage of people on here have blu-ray systems??