Let's run through an example. The limit of an amp or pre-amp for the output before clipping is determined by the supply rail voltages, and not by the gain. The gain is just the ratio or Vout / Vin.
Let's assume the maximum output of an amp is 20V peak to peak, and the amplifier has a "very high" gain (meaning enough gain to drive it into saturation/clipping). If we feed the input a 1V peak to peak single-ended signal, then the output will be 20V peak to peak (the upper limit of Vout). Now, if we feed it a 2V peak to peak differential signal, the max output is still limited to 20V.
So, the gain of the single ended input = 20V/1V = 20 (or 26dB), and the gain of the differntial input = 20V/2V = 10 (or 20dB). Thus, the voltage gain of the differential input is 6dB lower than the single ended input.
On the other hand, the input equation would be 20log(2V/1V) = 6dB, thus the input is 6dB "hotter" for a diff input as compared to the single ended input, but the gain is 6dB lower.
I'm sure this will get peer-reviewed soon enough, but I believe this is all correct. BTW, I took solid state last semester and am currently taking Linear IC (Op-Amps) this semester. So, I'm still learning too.