Although modern digital recording is much much better, there is still something that happens in the analog and vinyl domains that gives a pleasant result. There may be some creation of even-order harmonics that give it a warmth. There may still be some harshness in the digital world that our ears can perceive that we haven't learned how to measure yet. Our ears are analog and always will be.
Although I respect what Gio S is saying in the first part of his post, this second part is what always gets to me. When comparing formats under the premise "Does vinyl sound better" two sorts of answers pop up. One addresses the mathematics of the different of the two formats. CD has a greater dynamic range and higher frequency response. Sampling aside (because I've never seen the study that says that the same shlub can choose between CD and vinyl under ideal conditions reliably, but I'm willing to be enlightened) The CD ought to be able to capture the performance more closely, which would sound more realistic. This could easily qualify as better.
However, there is another sort of answer that crops up. It takes the form of "Vinyl sounds better because of extra-musical properties" or "Vinyl sounds better because of something that isn't/cant be measured, or just how it makes me feel." In my opinion, these answers don't qualify in the realm of this question, because they don't fit the scope of what we are dealing with.
Let me explain. Let's say I drive an original VW Beatle. It's in horrible condition, almost never starts without a a struggle, and has an exhaust leak in the cabin. You may ask "Lumps, Why don't you drive something better, like almost anything?"
In this case, If I reply that I can't afford anything better, I answer the question "why? If, however, I say "Because this car is yellow." I'm actually addressing the qualification "Better" more closely than "why? The car being yellow has nothing to do with its ability to operate; it's a reflection on my aesthetic preferences. That might qualify the car as better, but only under a skewed understanding of better. When we talk about better in reference to cars, it's logical to address the driveability, resale, safety, and such.
In back to the debate at hand, even if a vinyl recording has a certain extra musical something (better album art, nostalgic connections) These seem to be qualifications outside of the sorts of things we talk about when comparing the sound of one medium to another. If the breaking point was the ability to feature enormous album art and nothing else mattered, you can bet your grandma that CD's would be the dimensions of laserdisks and come in limited runs of production.
When comparing two mediums, we can also talk about artifacts, harmonics, distortion. My view is this. The medium that most closely represents the performance intended qualifies as the better medium, so long as the difference is audible. It does no good to nitpick over things that are beyond the trained ear's ability to perceive. This said, any additional distortion or EQ my provide a pleasing result, and may in fact be the intention of the artist. A vinyl may in fact produce a pleasant distortion (it certainly becomes distorted the more its played) and this may be in line with the performance. If it sounds better to the individual, then that is certainly one thing. This is the aesthetic preference of the individual. Go team. However, the discussion of which medium sounds better because its more accurate is a mathematical debate, and the argument about which is more pleasing is an aesthetic one.
Also, and not to pick on anyone, but the sciences of physics, audiology and the particular application to musical mediums are very well understood. We posses the ability to measure with stupid precision exactly what is happening when we turn data into sound. To think that there is something happening that is beyond the realm of our ability to measure when it comes to vinyl is a startling thought to me. I'd be interested to learn about a new type of energy transmission or interaction between a vinyl record and the listener, but I'm skeptical that there is anything going on that is beyond our ability to at least describe.
The above post is entirely too long and should not have been read by anyone. Also, the height of my nose in the air is entirely subject to interpretation.