Well maintained vinyl does sound better than CDs, especially the early CDs before they figured out how to get the bottom end in there (around 92 or so). Vinyl has a fuller and more complete sound, and it's also much more enjoyable in a ritualistic way to play than a CD (take it out of the sleeve, give a quick dusting, get it on the player, get the player moving, grab the needle and place... it's a great way to prepare your ears to listen to music).
Depends on what you mean by "better". The CD has to "sample" the original audio at certain rates/bit-depths, which can't be as high as the constant analog, which doesn't. But, vinyl (not specifically all analog media) suffers from physical wear, as CDs obviously don't so you have that trade-off, and at some point that same worn-out record will sound "worse" than the CD just because it's old.
If you were to sit down in a studio with professional gear (not micro-A/D/A converters) and listen to an analog master then to a 16-bit file recorded off it, you would hear an obvious difference. Now, put that analog master up against a 24-bit file recorded from it and one might be quite inclined to abandon the tape.
But, since most people don't have even "pro-sumer" gear, it doesn't even make much difference in that a small device will often make a high bit-depth file sound just like a lower bit-depth one. So, listening to a .mp3 and .wav file on a device that isn't that great makes no discernable difference to the listener, except that both are degraded in fidelity. At this point, some other reason, maybe economic, mass storage, convenience or random access are the key selling points.