If audio quality is the prime concern then attenuate+fixed gain.
If audio quality doesn't matter then attenuate+fixed gain.

The increased noise from the attenuate+fixed gain setup matters if it's perhaps a mic amp (they tend to have attentuators
and variable gain stages) - but if it's just plain old audio (you reference an LM386) the noise won't matter and stability is more important. Also, difficult to make an amplifier have a gain of 0 (when you want zero volume) and be adjustable for a gain of say x30 (max volume).