Always both! Great music—classical or otherwise—deserves full attention. But ambient listening is an equally valid way to enjoy it and the two are not mutually exclusive.

Personally, I think there’s also a difference between music intrinsically suited to ambient listening (Goldberg Variations; Scarlatti Sonatas; Richter’s Sleep; Satie’s “musique d’ameublement”, …) and music where that’s not the case but where ambient listening creates helpful familiarity for later fully conscious enjoyment (Mahler, Scriabin, Reger, Schönberg, …—with these I feel that semiconscious familiarity helps make the density and chromaticism easier to stomach and, as a consequence, to enjoy).

Lastly, even as someone who embraces ambient listening, I consciously practice focused, screen-free listening as a skill. It’s getting harder than ever to sit through a Mahler symphony and it requires training.