Eurofighter is really only good for peacetime patrols, the F35 will detect and shoot down enemies in real conflict far before the Eurofighter can do anything.
In a bizarre hypothetical conflict you would certainly not want to engage a F35 in an Eurofighter, the Eurofighter would be knocked out of the sky long before it could even see the F35. It certainly couldn’t turn on it’s radar.
There are extensive public studies available from e.g. the Danish government that ended up with the conclusion that the F35 is far superior in air-to-air combat. https://www.fmn.dk/globalassets/fmn/dokumenter/strategi/kamp...
Against China? If you’re willing to accept a level of losses we haven’t seen since WW2, but that’s just the nature of peer to peer warfare.