Since the chassis controls the weight of the car, and the F1s have the lightest chassis, it will have a big positive affect on the handling, but since they are also among the longest wheelbase chassis, they won't fit to many of the other bodies properly.
As far as the suspension, U won't notice much or any difference using the F1 chassis. It will allow U to set the ride height lower, but so will others, like the MRS Autobacs suspension, which also has a slightly higher grip value.