My perspective is that cds have always had the potential, and had the advantage spec capacity wise, to outperform vinyl and to be an excellent source medium but have failed to live up to their potential for several reasons.
One of these reasons or issues, as mijostyn already identified, is that the cd record companies virtually forced their recording engineers to mix their cds to attain a higher average SPL level which sacrificed the very good dynamics the digital cd format is capable of, resulting in 'uni volume' and the 'loudness wars'.
The cd format, after all, is just the lowest resolution current version of the lossless digital recording and playback format. As such, it still has numerous distinct advantages over both vinyl and reel to reel tape formats, such as lower distortion, lower noise floor, a greater frequency range and greater dynamics.
I have no reason to doubt teo_audio's claim that there is a fundamental flaw in all current analog to digital converters except for my personal experience listening to hi-res downloads recorded direct to digital and with minimal miking and mixing, mainly from The Sound Liaison Music Shop in Europe.
These are all recorded direct to digital as the music is played live at their fairly large studio that has excellent acoustics. However, I have no idea about the analog to digital conversion technology or equipment they utilize. I've only downloaded the 24 bit/96 KHz FLAC file versions thus far, but all of these recordings are clearly superior to the hundreds of ripped cd recordings on my hard drive. The most obviously superior attributes I notice are an extremely low noise floor, very high levels of detail, stereo sound stage imaging that is very well defined with a natural 'you are there' presentation and the naturally high dynamics normally only perceived on music played and experienced live.
I should also note that I have nothing against vinyl and know it can also be extremely good. I just perceive high resolution digital, that's recorded direct to digital and played back at 24 bit/96 KHz or higher resolution, to be superior in overall sound quality and a heck of a lot more convenient.
I understand that my post doesn't strictly adhere to the OP's thread question, but that's my take on what type of sources I prefer to listen to. I believe the fact that most cds are mixed poorly and very few are recorded direct to digital, explains why their overall sound quality performance level is not consistently superior to vinyl.
Tim