If you AM modulate the carrier f0 by a single tone f1, you get a spectrum with only three tones: f0 - f1, f0, f0 + f1. If you FM modulate it, well the thing get

If you AM modulate the carrier f0 by a single tone f1, you get a spectrum with only three tones: f0 - f1, f0, f0 + f1. If you FM modulate it, well the thing gets much more complex - depending on the depth of modulation you can get a much wider spectrum than from f0-f1 to f0+f1. So it is hard to compare. Your FM modulated signal may indeed be more resilient to noise but will require wider channel to be properly transmitted. I haven’t seen a convincing explanation if FM would be really that better than AM if both were given exactly the same channel width.