The main factor, is - as you mentioned - the SID, which was an amazing sound chip. For game programmers used to working on consoles, there wasn't much of a history of access to powerful sound hardware. As a result, composition quality on the console side took quite some time to catch up. Also, the availability of software specifically designed to control and compose music with the SID allowed the musically inclined to experiment with creating music on the C64, and many of these people were able to find jobs in the industry. There wasn't much of a chance to 'experiment' with NES or other console hardware. Finally, there wasn't a lot of overlap between console and computer game development teams during the 80s (all of the C64 console and arcade ports were outsourced to companies that specialized in computer software), so neither group directly influenced the other, at least until much later on.

There are some exceptions to the rule - Tim Follin's work on Solstice and Silver Surfer for the NES, for example. You definitely get some of that Commodore 64 music vibe, especially in the Solstice main theme (which is pretty much unlike anything else done with the NES sound hardware).