The Russian S-400 air defense system has been in the news lately. Turkey, India, and China are customers. The US is displeased and supposedly offered Turkey and India the Patriot system. How do the capabilities of these systems compare?
the S-400 is an anti-aircraft system and the Patriot is primarily an ant-ballistic missile system.
The Patriot PAC-3 has extremely limited range while the S-400 has very broad range.
PATRIOT is a surface-to-air platform. The original PAC -1 was anti-aircraft oriented. If you go thru the variants section of the Wiki Patriot article, it has a very good description of the missile and system evolution. It’s used together with THAAD for area and range coverage.
The S-400 serves a similar role. S-400 missile system - Wikipedia
S-400 uses multiple radars and missiles in the same general configuration.
The PATRIOT has more real world testing against missiles and aircraft. The Russians are masters of math/algorithms for radar systems.