I would think that the output voltages of the CDP would be matched with the input impedences of the preamp e.g 20/10KOhms for Balanced/SE, so I doubt if the Balanced would be significantly louder than SE.
Actually, the input impedance only affects the amount of current drawn by the preamp. The 2X voltage output for a balanced output (which is normal) will appear on the input of the preamp. You can verify this yourself with a test signal and a voltmeter.
Level matched comparisons are a pain to do and so most folks don't. Unfortunately, they end up comparing apples to oranges.
Looking at Bryston specs, Gain is 29dB/26dB for 1V/2V switches for SE/Balanced at their respective maximum input voltages. I would take this to mean the SE connection would be 3dB louder. (Yes/No?)
The BP26 does not have switch selectable input sensitivity.
I have never bothered about SE because Ayre themselves say in their manual that their Balanced connection performs better. I trust they won't say that without reason. If I am not mistaken all reviews on the CX7 and CX7e have all been based on using the balanced connection.
Nothing wrong with proper balanced lines. I'm a big fan. No reason not to take advantage of CMRR when you can.