I'm surprised this thread hasn't been made! So, lets look at the two arguments:
Pro-Analog -> Claim higher fidelity, "better" sound, organic, dynamic integrity
Pro-Digital -> Easier to work with, no imperfections because of medium, allows for more experimentation and new creative directions
Personally, I completely disagree that analog sounds better than digital. Firstly, the noise of a vinyl itself, plus the pops you get from the record player are enough to reject that. On top of that, the information lost in an Analog to Digital conversion - regardless of what anyone says - is (neigh) impossible to hear. In fact, the only real drawback I see from digital audio is the loudness war, which is entirely avoidable.
WE REPORT, YOU DECIDE.