You're going to find a fairly divided, imbalanced I'd think, standpoint on that.
And just to clarify, I'm under the impression that your question was in regards to the actual recording method and medium, not the gear producing the sounds, right?
My personal opinion is that Digital is the preferable way to go.
But first the problems with Digital... there is a technical loss of definition in the sound when recording digital. Sound is made up of curves, and curves are theoretically made up of an infinite amount of individual points along a path. We can't get our digital gear to truely reproduce those curves with full definition, so we lose a bit in the of the full sound and the differences in volume.
Another issue is on the headroom for recording. With Analogue recording you can raise the recording level into distortion, if done properly, to get a desired affect with minimal distortion or as stated, a desired distortion (Tape saturation). With digital recording, this headroom doesn't exist. You've got from -infinity db to 0db to record. When the levels reach more than 0, they clip, and I've never heard of anyone with a desire to hear digital clipping in a track.
Ok, I just sat here for a few minutes looking for another problem... can't find one so here's the pro's for digital/cons for analogue:
To truely record analogue, we're speaking on a magnetic tape. This medium has inherant problems of rumble and his. This are created by the very mechanisms that facilitate the recordings, and are difficult to overcome at the recording state.
Loss on rerecording is a horrible thing to deal with. When you take an analogue recording and rerecord it onto another tape, there's a bit of signal loss. This is impossible to defeat, though can be made less evident through the use of effect processors. But eventually, if enough transfers are made, the signal will become worthless.
The fact that the media used to record is based on magnetic tape (sometimes for digital as well though not always) is also of risk. If your studio happens to be attacked by large Electromagnetic Pulse weaponry, say goodbye to all your recordings.
With Digital recordings you have to deal with loss a bit less. Don't let anyone tell you it's lossless, all the digital tranfer media have error correction in place which points to the fact that errors happen. But the loss is much smaller than withh Analogue.
Once a transfer has been made to a digital multitracking system it becomes possible to visually edit the tracks, and process things multiple times. The true capabilities of digital recording and mastering are fairly open ended.
If one were to stay completely analogue, you'd be looking at a nightmare of patchbays and connections (all of which could open up the signal loop to noise and loss) to achieve some of the effect chains that are done simply with a digital multitracking system.
And now, of course from a perspective of possible costs involved in getting a work marketable, you'd have to eventually convert your recording to digital to have it pressed to CD.