Why does the Famicom sound different than the Nintendo?

Because of this.

The Famicom had two cartridge pins that were originally intended to facilitate the Famicom Disk System’s external sound chip, but were also used by cartridge games to provide sound enhancements. These pins were removed from the cartridge port of the NES and relocated to the bottom expansion port. As a result, individual cartridges could not make use of this functionality and many NES localizations suffered from technologically inferior sound compared to their equivalent Famicom versions. Castlevania III: Dracula’s Curse is a notable example of this problem.

And a taste of what the Famicom version of Castlevania III sounds like: