Amplus
If I understand you correctly - you r taking 2-ch stereo ANALOG OUTS from Oppo BD83SE via a set of Analog interconnects to an (Unprocessed) 2-ch stereo input on the Anthem D1 - which (I assume) in turn feeds (internally) to a 2-ch stereo ANALOG OUT from the Anthem D1 - using an additional set of Analog interconnects from the Anthem D1 to your pre-amp (or Receiver) in order to feed your main stereo speakers - is that correct? If so, I am curious what interconnects you r using for each run (& how long they are?)
If I have described this correctly - in this setup, you are listening with the SE upgrades to the ANALOG outputs, which SHOULD vastly improve the sound, as compared with the digital outputs, which are unchanged from the original BD83.
As to the 2nd part of your "test" - you say "and the other was the digital coax into the Anthem using just standard stereo" -
I'm unsure what that means? Do you mean the digital coax is running out from the Oppo to a digital input on the Anthem?
If so, what does "using just standard stereo" mean?
The digital out carries (up to) 7.1 channels - so do you mean you are listening only to the Front Left & Right channels ("Stereo")?
If so, I find it hard to believe that the sound is identical? I hope you understand that the SE mods on the Oppo have ZERO affect of the sound quality through the DIGITAL outputs (Only the Analog is improved)! So how could they be the same sound??