If there were a perfect way to capture the continuously varying sound pressure levels, and store them with at least the same detail as the number of air molecules involved, then analog would be lossless. But as it is, no analog recording media is a perfect representation of the source.
Furthermore, unless you're listening to a mono recording made with one mic, or a stereo playback of only two mics, there has been some mixing involved. Mixing done in the analog domain is more lossy than modern digital gear.
Plus, unless you have the analog mix-down master tape in on your player, you're listening to a copy. The analog duplication process is lossy. Digital duplication is not. Even more so, there's no analog storage media which is not altered (how ever so slightly) by the playback process itself.
Not to mention that the magnetic grain structure of 30 ips studio tape can't store as much dynamic range as 24-bit samples, or as much detail as a 192 kHz sampling rate.
Digital is superior in real world (not some imagined perfect analog media) from initial capture, to final playback. But only as far as it is handled correctly. Digital also allows recording engineers to quickly find peak levels, maximize those, and compress the rest of the signal to the point of lossiness. So digital's same advantage, perfect mathematical transforms, is its disadvantage, that it can be transformed in ways which analog cannot.
