I've owned Wadia gear before and last I heard was the 850, which I also like. But Wadia does volume control in the digital domain and so you need to jumper inside the unit to determine the max output level and then you shave bits down as you reduce volume. This is true of all the older gear. I can't speak for the 581 and the new series.
I find the Theta sound is warmer and more filled out in body than the Wadia gear I have heard but the Wadia gear has an amazing delicate top end (not that the theta doesn't) that is thinner but not Levinson thin. I find Wadia to sound more realistic than DCS or any of the other upsampling DACS. But I find that Theta even more pleasing in this respect.
I find the Theta sound is warmer and more filled out in body than the Wadia gear I have heard but the Wadia gear has an amazing delicate top end (not that the theta doesn't) that is thinner but not Levinson thin. I find Wadia to sound more realistic than DCS or any of the other upsampling DACS. But I find that Theta even more pleasing in this respect.