Brown noise
Has a spectral frequency of 1/f2, which means, in layman’s terms, that the noise has much more low‑frequency content. Its sounds are thunder‑ and waterfall‑like. Brown noise is so called "Brown" because, when viewed, the wave follows a Brownian motion curve. That is, the next sample in the waveform is equal to the previous sample, plus a small random amount. When viewed as a graph, this waveform looks like a mountain range.
Pink noise
Has a spectral frequency of 1/f and is found mostly in nature. It is the most natural sounding of the noises. By equalizing the sounds, you can generate rainfall, waterfalls, wind, rushing river, and other natural sounds. Pink noise is exactly between brown and white noise (hence, some people used to call it tan noise). It is neither random nor predictable; it is fractal‑like when viewed in a graph. When zoomed in, the pattern looks identical to when zoomed out, except at a lower amplitude.
White noise
Has a spectral frequency of 1, meaning that equal proportions of all frequencies are present. Because the human ear is more susceptible to high frequencies, white noise sounds very hissy.
Which one is better...up to you. I know what I use.