Just to clarify; vinyl does not provide any more "depth" or "tone" than modern digital formats. But compared to cassette, most people find the acoustic flaws of vinyl more pleasant than those of cassette.
(Whether the mixing utilizes the fantastic properties of digital formats is totally another matter.)
>This means that, by definition, a digital recording is not capturing the complete sound wave. It is approximating it with a series of steps.
>A vinyl record has a groove carved into it that mirrors the original sound's waveform. This means that no information is lost.
The typical range of hearing is 20Hz to 20kHz. Due to Nyquist aliasing [0] your sample rate must be at least twice the size of your overall dynamic range, which is why you have CD quality baselined at 44.1 khz, which is double your 20kHz and some extra to spare [1]
There are a couple of areas where analogue can still claim superiority. First is in digital reproduction quality is determined by the quality of your DAC [2], whereas analogue doesn't need this at all. Second is that you may reproduced "inaudible frequencies", in particular the "sub bass" [3] that you feel with your body beneath the 20Hz cutoff. I've been informed that these are often chopped out in the mastering process however so I'm not sure if that claim is legitimate.
[0] https://en.wikipedia.org/wiki/Nyquist_frequency
[1] https://en.wikipedia.org/wiki/Compact_Disc_Digital_Audio#Bit...
[2] https://en.wikipedia.org/wiki/Digital-to-analog_converter
In theory, yes. But practical analog systems are far from perfect, especially consumer formats such as vinyl. Just because analog system is not based on discrete samples does not mean that the original signal could be reproduced more accurately than through a digital system.