I think people often forget that PATRIOT is a long-range air-defence system with a range of 200+km for the PAC-2 missile (GEM/T, GEM+), which has limited ABM capabilities. It's blast-fragmentation warhead is a real turd when used against missiles. It's capability against small UAVs, at least in Israeli service with older PAC-2 and GEM+ missiles isn't clear cut either.
That puts it within the range threshold of S-400 against maneuvering, fighter-sized aircraft. And unlike S-400, PAC-2 has actual kills to its name.
PAC-3 has a range against ballistic missiles of 30km, but that's often erroneously stated as its range against all targets. Like seriously, the most common mistake I've seen is people saying PAC-3 has a range of 30km. It doesn't. Against aircraft and cruise missiles the PAC-3 missile has a range of 100km+. It's a proven ABM system and has, operationally, been used to counter UAVs and manned aircraft, including a blue-on-blue engagement during OIF where a USN F/A-18 was downed by a US Army PAC-3 battery
PAC-3MSE has a range that extends beyond 160+km (minimum, but expected to be further) and further extends the range against ballistic missile targets.
And unlike S-400, PATRIOT needs just one missile to achieve those capabilities, not four or five. Now S-400 still outranges PATRIOT, especially against tankers, AEW&CS, electronic warfare support, and other large, lumbering standoff air-frames, but the PATRIOT system compared favorable to the primary components of an S-400 battery.
Source? Once upon a time we wanted PATRIOT and
someone had to review the literature, and validate the tests and all that. Plus the Swede's are buying it and getting info from them is never hard.