Both the Typhoon and the F-22 were designed to dominate the BVR threat, defined at the time as Su-27, improved Su-27 and whatever the follow-on might be.
Both are better at that than their predecessors. However, until the fighter sensor people, the offboard-sensor people and the network-type people can defeat a well designed and functional stealth aircraft, the F-22 has a huge advantage and so far I have not heard of any tactical dirty tricks that can offset it.
However, it cost so much money that the RAF expects to have more Typhoons than the USAF has F-22s.