Well I can't speak about Rafale as I don't know much about it.
However in the A2A arena, NOTHING can be equal/better to the F-22 currently this is mainly down to its stealth really.
Against the F-15 and the F-16 the Typhoon in all honesty, wipes the floor with them in A2A. I don't know if it has "tango'd" with the F-16C yet but I do know its taken on the F-15 and defeated it every time, and the F-16AM (A's upgraded via the MLU programme). The F-18C also is no contest, however the F-18E/F its a bit blurred in the BVR due to the radars being pretty equal and same with the missiles... in WVR the Typhoon should still have the edge as it is more manouveurable and the ASRAAM's greater close range engagement envelope (instantaneous turn off the rail) compared to the 9X.
Just my 2 cents
Although saying all that... in the current technology arena, manouveurability is no longer so important.... new helmet mounted sights and the missiles such as ASRAAM, IRIS-T, Aim-9X its really whoever can get the opponent within its engagement envelope first is going to win.
Andy
EDIT: Did some reading, the Typhoon has faced the F-16C in WVR & BVR when competing against the F-15 and Rafale in Singapore... it was the ONLY one of the three to successfully complete all the A2A tests. The one the other two failed on where the Typhoon triumphed was a 3 F-16 vs 1 engagement.
The fact that Rafale didn't also triumph in that test also helps point to an answer to your question about the Rafale in relation to the F-16.