We run the Direzza 55 profiles on our race car.... We switched to them when we found out the difference in cost!! £360 for a set of 4 versus £450!
After a bit of calculation, we determined that the top of the tyre would be ~9mm closer to the inner arch and that the speed difference was ~3%. Therefore, if before you were doing 100 mph at a set engine RPM, you would be doing 103 mph at the same rpm. When on track, we didn't notice much of a difference at all AND if you're going to increase the power of your track car, it helps with gearing too.
In terms of clearances, we've cut away some of the bumper to make sure. We've also added caster, so if you don't do that you'll have a fair bit more room. Practically, we haven't had any problems on track, the only time we heard anything touching was at the bottom of paddock hill at Brands. In that case, we saw the bit of rubber mark on the inner arch, but it was touching a flat surface and for only a fraction of a second, so it wasn't a problem at all.
I'd highly recommend using the larger profile tyres, especially if you haven't excessively lowered the car!