This list of SNES extra chips on Wikipedia makes no mention of any sound chips on cartridges, but apparently some Famicom cartidges had ones.

I had a Sega Megadrive growing up, but I think the stock SNES sound chip was better than what the Sega had. I have a vague memory too that some SNES games had a sound chip on their cartridges, but the purpose of which was to enable the abuse of the original sound chip for non-audio processing.

I think in the end it might be that the Sega soundchip was more limited that what SNES had and thus the good songs had to be more carefully written and arranged to fit the limitations. I think one reason why Sonic 1 OST is so good it was made by a bassist as I think it's the bass that is most lacking on Sega games. But bassists tend to be quite sensitive to tone so I'm sure that helped.

Example: compare the hospital theme of EarthBound to the Star Light Zone theme, which seems to be Genesis chip bass at its most mellow and even then the bass line consists of pretty detached notes, I think in order to work around limitations. It works here because the music demands it, but I think SNES is the general winner here as it could support a bass and drum propelled track like the above.