I used to swear by the controller, and that wheels and alternate controls for games were really just gimmicks. My last wheel was some old clumsy thing I had for the Nintendo 64.
Anyway, I picked up GT4P and the logitech EX wheel in a bundle for like $75, rather it was given to me as a gift.
I take back every bad thing I've said about wheels, at least force feedback wheels anyway. When entering into a corner, when the weight shifts in the car, you actually feel it in the wheel as it fights against you the other direction, and can correct it with near pinpoint accuracy since you "feel" how much you need to fight. Whereas in the stick, most actions are in reaction to what you see on the screen, so I chalk up to the wheel being better in that regard.
If not for that, the immersion alone is just amazing. Every little bump, nudge, shift of car, etc. is felt through the wheel. Of course, what you encounter is probably heavily dependent on the quality of the wheel, but I'm having a blast with what most consider logitech's "budget line" wheel, the EX.
This was two days ago I started, and since I've attained the wheel I have a revived love for racers/sims, so for me at least it does make that much of a difference.