The spectra of pink and white noise are often a source of confusion. The difficulty arises from the fact that the spectra of these types of noise (or rather, their graphical representation) will change depending on the type of analyzer that is used.
Pink noise shows a flat spectrum when measured on a constant percentage bandwidth analyzer (such as a standard 1/3rd octave band RTA), while white noise shows as a straight line with a positive slope of 3 dB/octave and red (or Brownian, but not "brown") noise sports a negative 3 dB/octave slope. However, on an FFT analyzer white noise shows up flat, while pink noise has a downward slope of -3 dB/octave and red noise a slope of -6 dB/octave. This is because FFT uses frequency bins the bandwidth of which is the same number of Hz across the spectrum, so that, psycoacustically, at low frequencies bands are wide and they get narrow as we go up in frequency.
From a psycoacoustic point of view, the most relevant analyzer is one that shows pink noise as flat (no slope), since this relates more closely to the auditory system, which is akin to a band of one-third octave frequency.
The top figure shows the theoretical spectra of the three types of noises mentioned here as seen by a constant percentage bandwidth analyzer, the color of the curve denoting the type of noise. Next illlustrates the same, but seen by an FFT type analyzer. The lower figure corresponds to an FFT analysis performed on real noise signals (white noise is the green curve here).
Theoretical white, pink and red noise as seen by an RTA type analyzer
Theoretical white, pink and red noise as seen by an FFT type analyzer
White, pink and red noise as seen by a real FFT analysis