The question has everything to do with clipping. The only way what you said will happen is if you oversaturate the op-amp.
Otherwise it will reproduce the signal as best as it can given its slew rate and so forth - which is overspec for audio frequencies. Op-amp suitability for audio amplifiers goes on other factors, mainly how easy the IC is to work with, whether there are any peculiarities of the frequency response spectrum which make it undesirable, and what the noise behavior is like.
Most likely, the only reason that it sounds different is that you're generating a different signal. The gain is the cause but the gain is not the reason. You are altering the signal amplitude, and possibly the power response of the circuit.
Do you have access to bench equipment? Run a 2kHz tone into each amp then tune the volume divider so that the output signals match on an oscilloscope. Then listen to see what happens. They should be very similar. If not, you should analyze the circuit's power response in detail.
It's also possible that your op-amp (or other gain circuit) has different response at different gains...but you're comparing a small enough range that it shouldn't matter if it's stable at both. You can chart the frequency response out in LabVIEW fairly quickly at various gains to see, and it's probably in the data sheet, but I'm assuming that you specced parts which actually work at the set gains.