The analog sticks do require a fair amount of adjustment. I had to run many races with GT1 to make the adjustment, myself. I recommend making the effort. It's tricky at first, but as you grow accustomed to the feel you'll find your lap times dropping steadily. I think you'll enjoy the more precise feel as well - I also like that the sticks are easier on my thumbs.
I also use the right stick for gas and brake - the "analog" buttons are a bad joke, as far as I'm concerned.