I think your real question is wether uncompressed audio from a fine tuned DAC sounds better than compressed AAC converted by current Bluetooth headphones. The

I think your real question is wether uncompressed audio from a fine tuned DAC sounds better than compressed AAC converted by current Bluetooth headphones. The competition to this are mobile phones, and they almost all moved to bluetooth only, so the choice is which Bluetooth headphones gets better sound with a form factor you better like, pitted against the flurry of wired headphones and hybrid that are still on the market.