I compared the specs, and found:
C275 - Gain: 29 dB (that is about 1.23 V for 150 W 8 ohm based on my calculations)
C388 - Input sensitivity for line in to speaker out: 490 mV to give 80 W into 8 ohm, volume at maximum
My calculations show that the C388 will give the rated output of 150 W into 8 ohm with just 0.668 V input, that translates into a relatively high gain of 34.3 dB.
I think your point about level difference is valid regardless. Although the C388 has a higher gain, it is still possible that it is a volume matching issue if the OP did not use a SPL meter and a test tone. That's because those two amps may have totally different volume control characteristics. The C388 may still have to be turn higher up in order to match the output of the C275, but of course I am not speculating. The thing is, based on NAD's own published specs, there is no way the C275 could "blow the C388 out of the water". If the OP level matched the two to within 0.5 dB, I doubt he could tell those two amps apart.