On my FP Integra, I run a harder compound on the front of my car than I do on the rear, because of what Christian is describing. If I try to run the softer compound all the way around, the fronts don't handle the heat and abuse over a long run, and it starts to push. If I run the harder compound all the way around, then the rears take too long to come up into their operating temp range, and I'm too slow at the start of the race. If I try to change the setup of the car so its more manageable on those cool rears at the start, then it tightens up to much for the second half of the race. But with the hards on the front and softs on the rear, they all come up to temp pretty evenly, and I can set up the car so its kick-ass, stuck like glue, and consistent over long runs.
On my ITA Integra though, I can't do a R6 front and A6 rear setup, as the rear-end grip becomes too much. That car just weighs too much (300lbs heavier than the FP car), and the IT rules restrict some other things that I can do on the FP car, that I end up having to rely on lack of grip in the rear-end to help it turn. I've ran A6's all the way around on many occasions, but it only works when it's cool out and I'm on a track that doesn't abuse tire, otherwise it cooks the fronts. Also done A6's front and R6's rear, again trying to make the rear-end NOT grip, and that's ok at a place like Mid-Ohio, but its still an exercise in not burning the fronts off. One thing I never tried though was a 225 R6 front and 205 R6 rear setup, which might have been decent.