Hmm because J20 doesn't have TVC and does not have a higher T/W ?
Maximum T/W:
F-22 = 1.61
Typhoon = 1.76
Rate of Climb:
F-22 = 200 m/s
Typhoon = 315 m/s
Instantaneous turn rate/Sustain turn rate:30~35/>20(degree/sec)
In a one on one match within gun range I would hazard a guess and say Typhoon holds an advantage over the J20. It is about parity to Raptor WVR but only because the Raptor has 2D TVC but even then the wrong application of TVC could prove disastrous for the Raptor because of sudden and immense loss of energy and in WVR energy management is everything .
Interesting; the Eurofighter does have a very high T/W ratio; 1.66 for empty weight (I'm not sure how you arrived at 1.76) and 1.14 for loaded. The F-22 does retain a TWR advantage against the F-16 and Rafale, nevertheless. I agree that TVC isn't the holy grail for sustained agility, but can be a lifesaver at times.
The J-20 may not have TVC or adequate engines as of now, but if we are to assume that it will sooner or later adopt the WS-15 turbofans, with TVC and 180 kN thrust, its theoretical TWR with an empty weight reaches up to 2.08.