With 2.4v input, I would be able to reach the amps output spec at 6dB lower gain compared to 1.2v from the same unit under the same circumstances. That should clearly result in a better situation.
Depending on the design, that may not be the case. If you look at the ATI's, the gain remains the same regardless of balanced (2.4V) or unbalanced (1.2V). In the case of Bryston, there is a 6 dB difference in gain, but the output remains the same because they want you to flip that input selector switch, so the preamp volume position will be the same in each case, in order to get the same output from the power amp at the same volume position.
The ATI specs show the same SN ratio, the Bryston's shows 3 dB better with the input selector set for balanced input. I have read most of the S&V bench tests on power amps and noticed that very often, like 50/50, XLR didn't do better in SN, sometimes 1-2 dB better, somethings worse, overall about the same.
Balanced connection's benefits are for noise reduction in long interconnects, though for truly balanced amps such as ATI's top models, you can expect some reduction in even order harmonics. Still, for short runs of interconnects, the overall benefits of balanced connections, or even balanced amplifier from input to output, could be debatable. Like other things, it depends....
