CDs Vs LPs


Just wondering how many prefer CDs over LPs  or LPs over CDs for the best sound quality. Assuming that both turntable and CDP are same high end quality. 
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@atmasphere What I meant is, there doesn’t seem to be a exact consensus on what the EQ curves should be for older recordings in particular. As I understand it that is because the Labels themselves changed the recording process over time. Sorry if the question is off-topic.
RIAA, Decca, Columbia
As I understand it that is because the Labels themselves changed the recording process over time.
In the case of the RIAA curve, to change that the label would have to dig into the pre-emphasis networks in their LP mastering electronics. That's non-trivial since they are trimmed to match the cutter head in use.
However a label isn't doing well to deviate from the RIAA curve since most of their customer base won't have access to equipment that has their curve- in a nutshell, its a non-starter.

The older EQ curves- Decca, Columbia and so on won't be changing, since they've not been in use since the early or mid 1950s.
I got back into vinyl about ten years ago. I’ve had a few Arc phono stages and finally ended up with an Asthetix Rhea Signature, going into an Aesthetix Calypso Signature.  There are many better preamps, but my budget won’t allow and I’m satisfied with my setup.  I have a Koetsu Urushi Black and a Dynavector DRT XV-s1, as my carts and am using Verastarrr Silvrstream phono interconnects.  My CD player is a Theta Miles.  I like the sound of vinyl, specially when I first start the lp.  I hear a sound that envelopes me, that I do not hear with CDs. I have been doing an A/B comparison, playing the same title of a cd and lp, cuing each at the same time.  I go back and forth to compare the sound.  Maybe it’s my hearing going away, but it’s getting harder for me to diffienturate between the two.  Most lps have an ambience, that a cd can’t provide.  I’ve said this before-wish I had a good RTR with some prerecorded tapes.  That’s the best sound I’ve ever heard.

A "analog" or LP rig is much more expensive when it exceeds CD. In other words, a 1K CD player will sound better than a 1K record player. It requires an outlay of at least 3K for the record player to exceed the CD.

As you know, there are many who pay that much for a cartridge; with that kind of cash outlay, they should sound better than CD.

There are some wild cards in the deck; they are the CD's that sound better than LP's. CD's are variable, as are records, but in general records "played on expensive rigs" sound better than CD's, while records played on cheap rigs don't sound as good as CD's.

"Vinylites" or "analogers", are evangelical in their zeal to spread the word about those black discs; they will tell you that a record played on a cheap record player will sound better than CD; it just ain't so.

If you got the dough, you can make it go; if not..... This is a case of run with the big dogs or stay at home.
CD is fundamentally flawed from a standpoint of being incapable of faithfully reproducing the original analog content without the staircase effect and artifacts. No amount of money spent on transports and DACs will ever change the fact that it uses substandard 44kHz sampling.