It used to be rather popular, actually, to play at pawn-and-move odds. If you search through old games, you'll eventually come across one where black starts without an f pawn.
There's also a famous Capablanca game where a young Capablanca is given a queen by his opponent (he wins, of course.)
I'd say the two biggest problems with chess are:
1. Too many draws.
2. First move has too big an advantage.
Neither of these is a problem in Go (draws are extremely rare or even impossible in many rule sets, and the second player is now given enough points that the game is almost even.)
I like both games a lot. Arimaa is fun too.
It's like you can see the player's minds working sometimes (maybe if I was better it would be more often), an interesting game to be sure.
I don't know if it's true, I could just be stealing a line from the movie Pi; but people in a movie once said that no two games are like, and thus the game serves as pseudo microcosm for the universe. Either way you should watch that movie: http://www.imdb.com/title/tt0138704/ , and give the game a whirl.
[I always had trouble with chess, my "ADD" always got in my way. I'd end up making a mistake I had previously ruled out, because I had forgotten where I was at, felt rushed, and eventually just made a move.]