I have been carrying out CD vs Vinyl on different TT > Tonearm > Cartridge combinations over the past few years.
In the same way a TT > Tonearm > Cartridge can sound very different to each other, adding the CD replay into the equation can also show a different emphasis on a recording.
I have also got a Pre Amp with Two Inputs only for this experience and can set up the CDP to almost share the same replay as the LP.
Swapping Sources is just a one click operation, and I have Albums that are almost parity for the Volume setting and Albums that can require a few clicks on the Volume to achieve a close volume match.
I have not got too lost in which is the best, as either has areas within a recording that can be an attractor in comparison to the other.
I have come to a stage where I ask which Source is the most desirable to be lived with if the replay is left to run on from one Source.
With this method, the extended listening is usually settled into within a Track, and the other Source can be left without need to be reintroduced.
This experience stands for both Vinyl and CD, neither has a place of superiority when the SQ is assessed for the attraction it produce during a presentation.