If you try for an exact port, it will sound a bit different, even if you use trivial samples (square, triangle, and noise). The NES APU generates mostly squarish waves at 894.9 kHz through a set of five primitive DACs (digital to analog converters) and relies on analog post-filtering in the console and TV to remove high harmonics. The Super NES S-DSP generates Gaussian-interpolated waves at 32 kHz through a pair of DACs with higher bit depth. Because of the lower sample rate, it has to filter out the high frequencies before sending them to the DAC; hence the use of Gaussian interpolation. But the Gaussian formula saps a lot of the treble, giving the S-DSP a "dark" or "muffled" sound unless you take care to preemphasize your samples properly.
But in practice, it sounds how you want it to sound.
Super Mario World and
Super Mario All-Stars use a completely rewritten engine with rearranged music, and "Here We Go" from
Super Mario Bros. sounds like
this and
this through it. Later games would re-remix it:
Super Mario 64,
Super Smash Bros. Melee,
Dance Dance Revolution Mario Mix, and
Tetris DS.