The ultra modern '5th generation' fighters tackle a lot of your criteria with regard to agility by being deliberately unstable. It might be a bit dramatic to say that the eurofighter typhoon (poss '4th gen'?) and the raptor would fall out of the sky without the computers that work the fly-by-wire controls, but they are kept stable by the computers so that when a command is entered by the pilot they are just waiting to get all twisty.
In a guns only environment a spitfire would easily turn inside later fighters like the lightning and the tornado but would be interesting to see it up against a typhoon with all its fancy tricks, or a raptor with it's directable thrust.
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