The pink/white noise and analyzer thing is confusing as hell. Start with the analyzer. There are two kinds. We've traditionally used 1/N octave analyzers, which are called constant percentage bandwidth (CPB) instruments or relative bandwidth instruments. 1/3 octave made sense because you didn't have to build too many filter circuits. 1/10 octave was also popular if the unit didn't have to work in real time, though with opamps even those are easy now. If you analyze pink noise with a CPB analyzer, it displays flat response.
When FFT analyzers were developed they were constant bandwidth devices. If you analyze pink noise with an FFT analyzer, it will show a falling response because the signal power at a constant bandwidth falls off at 3 dB per octave. So, with an FFT analyzer you need white noise to display a flat response. Of course every FFT analyzer is based on a processor, so many of them can convert from constant bandwidth to constant percentage bandwidth.
I hope I got that right, because it's still confusing. No doubt somebody will fix it if I didn't! Bottom line is either analyzer will tell you what your system response is, but you have to use the right signal for the type of analyzer you're using. Flat electronics/system will be correctly shown to be flat with either type of analyzer, if you use the right noise source. If you just listen to the noise sources, pink noise is softer and more pleasing than white noise.
IMO, 1/3 octave analysis is way better for looking at speakers and rooms because it simplifies things and ignores narrow resonances and dips.