I don't have experience with the Rega DAC, but the Wadia 12 was great. I had it for 20 years. Strong points: dynamics, liveliness and drama, as well as neutrality. Resolution was pretty good, but no match for my current Berkeley Alpha 2 DAC, which also excels in the areas mentioned.
In terms of liveliness, drama and neutrality it easily beat in my system modern alternatives like NAD M51 and Hegel DAC25. Warm and full sounding recordings are reproduced as such, colder or thinner sounding ones also (just like on the Berkeley). It doesn't pretty up things, which I like. I don't want all recordings to acquire a boring sameness. -- Bass is very precise, but on the leaner side of things, compared to modern DACs.
Caveat: mine was upgraded with a Wadia 860 opamp. More silence between the notes. I don't know how the stock Wadia 12 would compare to modern alternatives, but it still would have the positive attributes I just described.
You can get an old Wadia 12 very cheap these days.