ZSnes(Win) can run games like Bomberman or Goof troop across internet or LAN so you can play with friends without having to be in the same room, on the same keyboard. However, within minutes you will experience a De-Sync. The problem in this is that both connected computers are trying to "host" the game for the sake of speed,. while 1 should be the host, and the other the "slave".
Higan, originally BSNES, was built with the goal of 100% cycle-accurate SNES emulation. This ensures that games play exactly as they were on the original console, including low-level hacks requiring precise timing (such as shadows in Air Strike Patrol), to a degree not possible in any other emulator.
Byuu, the author of Higan, went through the effort of acquiring all Super Nintendo/Super Famicom games with extension chips, and de-capping and reverse engineering those chips, to ensure perfect, cycle-accurate emulation and flawless support for every game ever released for the console.
In order to achieve such a high degree of accuracy, the emulator requires significant usage of system resources. Because of this, a system with a fast processor and a fair amount of RAM is necessary - Higan isn't recommended for use on older machines.
If you've used an emulator on anything that isn't a PC, you were likely using SNES9x. Unlike most competing emulators, SNES9X was built to be ported to any architecture.