Peter > Homer
i don't understand why you people say 'Homer is a better written character, so he's funnier'
Peter does random, stupid s*** that's hilarious, i could care less if his character's 'back story' has more holes in it than Homer's.....
Well to enjoy certain forms of comedy it has to have strong writing. Peter's character only works in that form, act retarded, make pop references, zany flashbacks etc. Other than that he is a shallow 2D character who changes from episode to episode as pointed out, I agree he is funnier but that doesn't mean he is a deeper character and what this leads to is less funny material.
You can revolve a show around Homer, you can build seasons off Homer (Simpsons went strong a good 6 years) you can't say the same about Peter who is already beyond stale and needs Stewie and Quagmire to make a solid show.