Well that's good because they are both theoretical nightmares. The Grunfeld is more played at top level, at lower level it is almost unheard of. It is sharper and more theory heavy. It is also unbelievably complex and confusing. You give white the center and then try to tear it down but you have to be precise. There is also some forced lines that lead to a draw I believe and it can be somewhat avoided. You can check out some games by Peter Svidler and Maxime Vachier Lagrave.
The KID is always popular even at low elo. It's a little more flexible and you get closed position with a locked center so pawn play is everything. You also should be comfortable to play with a lack of space. It can get really aggressive and there are many systems for white but the ideas are simpler to grasp. Radjabov plays this today, you can check out his games.
Of course you should try them out see if you have fun with them. And these types of posts usually attract those "you're an idiot for learning openings under 2500 rating" but just ignore them.
I'm hoping some stronger players can give me a summary of the differences between the King's Indian and the Grunfeld, their theoretical soundness, your preference for one or the other, and, if you are a KID or Grunfeld player, how you play against other systems like the London/ Trompowsky, etc. I currently play the semi-slav, and have had success with it, but I have been experimenting in blitz with system like the Pirc and Grunfeld, and am really enjoying the counterattacking possibilities and, believe it or not, dealing with raging attacks from White. Still, I want to focus in on either the KID or Grunfeld against d4, and start building a comprehensive repertoire around one of them, if possible. I'm obviously not afraid of heavy theory.