The reason artists like Lady Gaga prefer analog tape recordings is that there is no risk of unbearable clipping that happens with digital recordings in live recordings as an example. Analog recording will accept sound level overload situations to a certain extent, but digital ones won't, and there is no practical way to correct the situation when distortion has occured.
This situation happened with so many digital recordings that we can hear on CDs. This, of course, all depends on the experience and competence of the recording engineer. The situation is more critical with classical music recordings where the dynamic range can reach up to 35db, on one opera recording which I was informed of.
I have noticed that the quality of the recordings on films, concert DVDs and Blu-rays is of a better quality and so far, I don't recall having heard a multichannel DVD or Blu-ray reproducing noticeable distortion. The fact that DVDs and Blu-ray are using a 24 bit depth instead of 16 bits allows more dynamic range and surely helps with the end results.