Digital has a far greater dynamic range and precision, especially if you include high bit-width or double floating point & high sample rates. There is no limit. You could model any sort of 'analog distortion warmth' which is often what is appealing about analog sound. On the other hand, someone who is willing to put the effort and money into printing vinyl will likely have it mastered specifically for vinyl. So my feeling is that there is a lot of low-effort digital music pushed out into the world that is just shite. And maybe overall, vinyl music has good quality just because people are more careful? I'm sure it also depends what you are listening to. Soundcloud rappers don't even need quality if they've got Gucci shoes.
Yes. (I say as someone who mainly listens to vinyl, because I own it.)
Intrinsic limitations of the medium mean that it's more or less impossible to get a signal to noise ratio of more than 75 dB, channel crosstalk under -45 dB, or THD+N under 0.1%, or a frequency response of about 30 Hz to 13 kHz plus or minus 1 dB
Even a mediocre CD player will do 80 dB, -70 dB, 0.01%, and 20 Hz - 20 kHz plus or minus 0.5 dB respectively. Most of them are better than those numbers.
And once you get to or above 192 kSa/s MP3, let alone more modern CODECs, you can do better still.
Can you hear the difference? Absolutely. Many people prefer vinyl because it sounds "warmer", or because the hiss and crackle bring on (movie-induced?) nostalgia for their childhoods.