Total Harmonic Distortion (THD) is the most common measurement of distortion. THD is a measurement of nonlinear distortion -- where amplifiers/transducers actually change the shape of the sound waves via new tones at the output signal not necessarily in the input signal. Acceptable THD for me (my audible limits) is
Sound to Noise Ratio (SNR) is the most common quantitative measurement of noise. It is simply the ratio of signal strength to noise level. Noise, both interfering signal and random noise, is an error that does not correlate with the input signal. With a SNR less than 40 dB, you will hear audible noise during most playback. When SNR is greater than 55 or 60 dB, then most noise will only be heard during quiet passages. Usually a SNR of 90 dB or higher is more than adequate. However, in very quiet car, some people can hear noise with a SNR as high as 96 dB. If this were true with jtmoney, he was hearing the Brutus's noise (the BX1500D has a SNR of 95db), not distortion.
Still, neither SNR or THD measure linear distortion, of which changes the frequency response (amplitude) and phase response (timing) of your music. Luckily, these can be compensated for (yet, IMO, shouldn't need to be) without buying new amps.