will all season tires affect autoX performance? hell yes.
How much will it matter? If you are in a street tire class and want to be anywhere competative, you will need one of the aforementioned Max Performance summer tires.

Another one to add to the list:
Bridgestone Potenza RE-01R, these are now at the top of the pile as far as performnce tires from bridgestone. The S03 is being phased out.
The falkens are still probably your best bang for buck (unless you can find the others on a special).
Whats been said about wet weather driving is correct: slow down. In fact even if you have all season tires, slow down!