I would not choose the Wadia DAC unless you were willing to also get a really nice external linear power supply such as a Teradak (instead of using the switching power supply adapter that comes with the unit). Though, it’s only driven by a +5V DC power supply, so the analog circuits are not going to have the optimum voltage for operating (which is typically a split power supply such as +/-12V or more).
Based on this, I would choose the Wyred 4 Sound over the Wadia. The Wyred also has the extremely large 88,000uf power supply. Translates into much stronger/fuller bass, fuller midrange, no leanness.
That being said, I have not heard either DAC, so I don’t know the sonic signature differences.