Basically, it's a trade-off between performance and accuracy. Snes9x has better performance, at the cost of a loss of emulation accuracy (which could mess up a few games), while Higan has better emulation accuracy, at the cost of performance (IIRC, it requires at least 3 GB of RAM, which is quite a lot for a SNES emulator).
If you don't care about either and just want to play some SNES games, go with Snes9x if your specs aren't that good. Otherwise, either emulator is fine.