I don't have any experience with the Wyrd, but I have a MacPro connected to a Bifrost DAC and Asgard 2 amplifier running to a pair of Sennheiser 650 headphones (work/live in a noisy environment). Completely satisfied.
I suspect that the newer cheap amps such as the Vali and Magni 2 have fixed these issues.
I can absolutely tell the details in certain albums using the new setup. Hearing the difference between FLAC/ALE and something encoded at 320bps or higher is really dependent on the material though.