With the Oppo I’m using HDMI, with the Jay’s AES/EBU. In addition, the Jay’s goes directly to my Berkeley whereas the Oppo goes through a GeerFab HDMI converter. Given there are differences, CD’s sound better through the Jay’s. I bought the Jay’s just for CD and I’m thrilled with it.
Regarding HDCD, at the time I bought mine their website didn’t address HDCD. I asked them about it, and I really didn’t think they understood what I was talking about. While they gave me a bunch of double talk, they finally did address it on their website.