The SID chip in the c64 is very unique, it's specifically designed for music versus the PSG-like square wave generators in other systems at the time. (I will say the Atari POKEY is magical though.)
Comparing c64 to Amiga isn't fair, the Amiga was a generation later. What the c64 should be compared with is the Atari 8-bit systems (400, 800, 65XE, 130XE), Apple II, Colecovision.
Having the 64k RAM, plus sprites, plus a sound chip that implemented ADSR and different waveforms other than square did introduce a lot of possibilities and excitement in 1982 though, even if you tried your best to use them from the absolutely shitty BASIC and/or had to wait minutes for things to load from disk or cassette.
Comparing c64 to Amiga isn't fair, the Amiga was a generation later. What the c64 should be compared with is the Atari 8-bit systems (400, 800, 65XE, 130XE), Apple II, Colecovision.
Having the 64k RAM, plus sprites, plus a sound chip that implemented ADSR and different waveforms other than square did introduce a lot of possibilities and excitement in 1982 though, even if you tried your best to use them from the absolutely shitty BASIC and/or had to wait minutes for things to load from disk or cassette.