Analogue has decreased in popularity over the years for a number of reasons. The cost of digital recording is often a lot less as not many people have analogue multitrack tape machines at home, so in order to work in that medium professional studio costs must be incurred, which can be prohibitive. By contrast, it's easy to have a digital home recording setup. Getting things to sound good will take some practice of course.
I've done quite a few albums where I've recorded the basic tracks to tape, then transferred those to Pro Tools and continued overdubs in there. I certainly don't feel that digital recording has any less depth than analogue though. I think you can find flat (as in one-dimensional) sounding records that were recorded and mixed in a 100% analogue environment.
By the same token, digital can also sound warm. It's really all about the sound you're going for, and it's easy to make something sound soft or hard, clear or muffled, using EQ, compression etc.
I have no real preference in the end, and am equally happy to work in either environment. I've done a lot more albums in the analogue domain than in the digital, probably about 300 analogue compared to say 70 digital. I do enjoy the editing and manipulation capabilities of digital, but as I mentioned, tracking on analogue and then transferring to digital for editing etc is also possible, so one could easily have the best of both worlds if desired.