From a sound design point of view, digital recordings are a lot easier to edit and this opens up a world of possibilities for us. For example, editing in a DAW can be done pretty much visually but splicing tape is an art that, from what I've heard used to take years to master.
And from a storage point of view, studios used to be clattered with bits of tape hanging from every available surface. There was no search function or tagging and very importantly, no non-destructive editing.
You also get a larger dynamic range (not that you really need it because everything ends up squashed by compressors and limiters these days)and noise becomes much much less of a problem.
This doesn't make analogue recording technology obsolete though. I can't pinpoint what it is but analogue recordings or even digital ones that have gone through some (decent) analogue gear tend to sound less clinical and somehow more pleasing.
Also, this doesn't mean that everything digital will sound better than everything analogue. When we make the comparison, we use PCM as a representation of a digital recording. But music that most listeners listen to in digital form has had a lot of data compression in most cases.
So if we compare the quality of the sound that reaches the listeners' ears, (how many would notice audible artifacts) the quality gap somewhat narrows.
Another thing you can compare is how well they age. If we compare CDs with vinyl, none of them age very well indeed but a big difference is that you can listen to a scratched record much easier than a scratched CD.
There is no right and wrong in music. I personally like tape distortion so I can't see anything wrong with recording something to tape just to get some niceness out of it and then back to DAW for editing digitally to publish online. So my first choice would be to have both. Next choice to have digital only and last, to have analogue only because as much as I'd like to try splicing as a hobby, I wouldn't want to have to work that way.