The whole sine wave/square wave/sampling thing is tempting, but I feel the "warmth" thing calling my name.
Warmth has nothing to do with sine or square waves, warmth in vinyl comes from the inherently high THD in the output of turntables, phono cartridges, and usually the preamps made for these rigs. It causes a thickening of the sound, which people tend to find pleasing. In particular, warmth is the thickening of the lower registers. Personally, I want the most neutral and accurate reproduction possible, which goes hands down to digital.
PS. I'm not going to respond to anything else most likely, I don't want this to turn into a flame war, I just want at least some of the fallacies and hocus pocus surrounding vinyl cleared up. Sound is a science, we have studied it extensively, and we know how it works, and why. It's fine if you just like the way vinyl sounds, but it's not fine to believe it's objectively superior to digital, because that spectre has been objectively dispelled ages ago.
Though that might make you think I hate vinyl, I do own vinyl copies of several Skinny Puppy albums, most notably a sealed first pressing of Last Rights that's never getting opened. :P