I always hate these kinds of discussions when there are too many engineers in the room. Of course, digital is better. You can prove it with Nyquist's theorem. In the long run, digital will win.
That said, there are numerous implicit signal-changing steps which tend to happen with analog equipment that people often find pleasing and which are not/haven't been sucessfully emulated in most digital audio equipment.
Take guitar amps. I've got a couple of decent Roland digital amps. They do an OK job of modelling a few different old tube amps. Do they sound like my friend's old blackface quad reverb? Oh god no. There is some magic going on there that the digital guys haven't figured out how to reproduce. Even vs. odd harmonics? Yeah I think we get that now, but there's more in there and we're not successfully modelling it. I can enumerate a lot of factors we're probably missing(power supply brownout at high volume, capacitive and inductive feedback loops, tube nonlinearities, transformer nonlinearities, temperature fluctuations, microphonic components... etc etc etc) but there are still more we haven't really considered yet.
That said, there are still people who prefer solid-state guitar and HiFi sound to analog colored sound. A lot of it is what you're used to. People hear different things, sometimes due to culture, sometimes due to physiology... it's complicated.
Back to vinyl records - they do have a nicer sound in many cases, clicks and pops aside. It's probably a result of the RIAA EQ and the physics of a needle riding over vinyl, but I don't really know. One thing I do think has value is the act of listening to a complete record. Not only are you appreciating the artists' complete work as they intended it, the ritual of listening to a record often entails setting aside time and space to solely enjoy that record. You can't compare listening to, say, Dark Side of the Moon, while lying on your couch in a dark room to listening to a few out-of-context songs on your headphones while riding a bus.
Whatever... we aren't going to solve this battle on /.