Amiga can do pretty nice sounding SID renditions (Per Hakan Sundell's C64 Demo for Amiga OCS and his SIDPlay app sound excellent...he also wrote C64S DOS emulator).
The problem with having a traditional soundchip is they have a distinct sound. The SID suffers a lot less from this than the Yamaha AY/YM Amstrad/Atari ST chips but designing tunes for games on Amiga you forget how spoilt you are when you then have to do the C64 version as well. All AY/YM tunes from the Amstrad/ST are instantly recognisable (as are the TI chips in Coleco/MSX machines too) but there are a lot of instances where the SID is not recognisable (compare the soundtrack to Rambo for example with the soundtrack to Sanxion's loading music to the electric guitar solo in the game Wizball. You can guess the author but the layman in the street would not know they are on the same computer).
Having said that SID is a genuine analogue synth on a chip and that is the key to why it is such an awesome piece of kit to design things for. If you look how much 1980 mono synths with similar technology cost you will not call a $20 6581 chip over priced ever again IMO

Biggest problem with SIDs IMO are that no two even from the same revision sound exactly the same ie two 6581 revision 3 chips may sound different even in the same machine...a subtle difference but with games that use complex filtering effects it can be noticeably different.
Any way if you really want to see what all the fuss is about you need to get a silver label original 1982 C64 with ceramic VIC-II chip and take it from there, later models of the C64 produce a much less basey sound which makes SFX in games sound a bit weedy lol
Avoid the white 64C with the 8580, totally useless machine unless all you want to do is run Cynthcart/Prophet 64 for basic music work.