NACS's plug is smaller because the primary pins support both AC and DC. CCS uses separate pins for AC and DC. Also NACS locks the cable on the car side while CCS locks on both sides. That means with CCS, a malfunctioning cable can strand your car.
The main downside of NACS is that it doesn't support three-phase, but neither does CCS1, which is the version of the CCS standard used in North America and Japan (where household three-phase is rare). Europe uses CCS2, which is an even larger connector than CCS1 (due to the extra pin needed for three-phase).