Minidisc uses the ATRAC compressor which, at least after ATRAC-4, is quite
reasonable. But it's proprietary, and Sony guarded that jealously[1]. They
wouldn't tell anyone anything about the workings (not even those of us
working for a Sony Multimedia company...). So MP3 got better support from
everyone else, and the rest is history.
Vic.
[1] I once wrote a rebuttal to ZDNet after they'd published an article
claiming that Sony's iLink was a proprietary audio compressor. Sony let me
write that iLink was a networking technology not a compressor, but
wouldn't let me write that it was just IEEE1394...