Not much, really.
Shiny's grey(er?). Of course shiny Gengar would sparkle when entering battle.
Gengar - Pokedex - this is the kind of stuff you can check on the Pokedex on this site. All entries have the Pokemon's normal sprite and shiny sprite.
This is the normal one
This is the shiny
As you see the shiny is darker and less Colorful. The normal Gengar is more purple.