This article is in the process of being written and refined.
The Big Questions
What do consumers want?
I think the average person would only care to differentiate mixes of a recording; that is, mono vs. stereo, remix vs. album edit vs. radio edit.
What do nerds want?
Some nerds want to be able to identify audio down to the bit-level; that is, accessing dynamic range information for a piece of audio (e.g., a track on a CD); viewing a waveform representation of said audio; a hash of the (digital) audio, for lookup purposes.
Otherwise, some nerds want to be able to discern different masters of particular mixes--perhaps a 1970s master vs. a clipped 2000s master or a 2000s master with far less dynamic range. Not at the anal bit-level, but close enough.