Admiral Beez said:
We're comparing one plane, with one pilot, with no outside help against another under the same circumstances.
All restrictions you failed to put in your original scenario!
Quit changing the qualifications just because you don't like the answers!
OK, having made sure that you have eliminated the western equivalents (F-11 Tiger, F-8 Crusader, Dassault Super Mystere... all entered service in early 1957) by carefully setting your scenario for the only full year in which the Mig-19 (mid-1955) was around, but not its equivalents, then I guess it wins by default.
After all, the Mig-19 can choose to engage/disengage the F-100, Mystere IV, Hunter, Javelin, Swift, F4D Skyray, F3H Demon, etc at will by virtue of its better top speed and climb rate.
Congratulations.

