I don't know about advantages. Sometimes (but not always) vinyl just sounds better. Partly due to the work of the mastering/cutting engineers work, of course, - and partly due to the fact that less definition is lost when transferring a hi def digital format directly to vinyl.
It has been discussed here sometimes how certain American re-pressers allegedly cut corners and use CD-masters instead, but I'm unsure whether this is true or not. In any case, re-release can sometimes sound way different than the 1st ed. And it can go both ways (re-mastered re-releases sometimes are superior to the 1st ed.)
But yeah, when you start to really listen to how they sound, especially compared to MP3s, you either like the difference or you don't.
And I admit that you have to have a decent hi-fi setup for it to matter a lot. Which is a rather expensive thing to have.
I still buy CDs btw, so it's not like I'm totally against digital formats or anything. But I only buy mp3s as a last resort, - which almost never happens. The current freebie-marathon being a notable exception.
A more aesthetic reason would be the pacing of sets, that come out specifically for the vinyl format.
Like for intance Sherwood and Pinch's new "Late Night Endless" 2LP album has a huge difference between the two discs (the first LP being more hostile/aggressive, the second decidedly more trippy and laid back). Simply playing the whole thing as a digital playlist would undermine this effort of track pacing and moods. I usually only play one of them, dependant on my mood.
With stuff such as Sgt. peppers, where the transission between the two sides of the album is a major part of the release, the effect is even more pronounced.
Oh, and the covers are potentially way cooler than a stamp sized pixel blur on a smart phone if you ask me;)
There are admittedly a lot of disadvantages with the format. Size, handling etc. And stuff like I just had to buy a new copy of one of my favourites, simply because I accidentally dropped it, making track one unplayable. So perhaps not the best format if your a stumblebum like me;)