Well I'll try and do a more careful listening test later today. Yesterday I was primarily testing the JDL Atom vs. my 18 year old MG Head DT (computer source, optical output to an Entech 205.2 DAC). I tried to A/B it as best as I could without special equipment; got the two amps matched in volume (to 74 dB using a 1 kHz test tone with an SPL meter I have - I wonder how many people actually bother to do this, volume levels make a huge difference). Between those two amps, I couldn't tell a difference after listening to various music for an hour, which was a disappointment, I had expected to hear some difference, especially since it was tube vs. solid state. At the end of my test I just randomly plugged the headphones into my iPhone (through its Apple supplied lightning DAC/amp dongle) and I couldn't really tell anything was being lost, but I admittedly did not do a careful listening to it (but then again - if it's not an obvious change, does it matter?)
Now certainly, the Anandas are different than the HD650s they are replacing. I am enjoying the much greater soundstage and upper range clarity.