Why does FM sound better than AM?

There are many differences that explain why one can be better. All else being equal:

- bandwidth of modulated signal: it is better to spread the signal over a large bandwidth => Nlog(1+snr) > log(1+Nsnr). the bandwidth used by the FM signal is larger

- wasted energy on the DC signal: AM signal is A + s(t) where A > abs(s(t)) to make sure the sent signal is always positive. A (DC) does not carry information so the effective signal to noise ratio of a DC-less signal should be higher (phase/frequency modulation, signalling that can detect the negative part...)

- filtering of baseband signal => if you filter too much the original signal, you lose information even before transmission. Voice is usually filtered and 4KHz, but music needs more. FM has more margin (more allocated bandwidth) so can have less stringent filters

- tolerance to fading: the wireless channel is not AWGN, it is frequency dependent due to multipath. While radio signals are relatively narrow, signal modulated in frequency are more robust to fading (OFDM...)