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.