I thought the F-35 was not fielded yet ... but it might be me.
EF and rafale are not ment to rival the F-22 - since its assigned to a different role.
Eurofighter is a capable platform but cannot outperform the F-22 in anything but external load and turning capability. The F-35 certainly will neither. Rafalle is a way less capable and way less expensive airplane then the EF.
AESA capability still lacking in rafale as well as eurofighter makes them a whole class inferior - but EF excells with magnificient aerodynamic performance (can outturn an F-22) and supercruise capabilities (slower than F-22 but the only plane second to the F22 at all capable to do so)
AESA shall be added in the future but military projects have a legendary record of beeing delayed and over budget. (see F-35 - new method of budget controll)
A special topic is stealth.
Stealth is just a word for obscuring the plane to sensors like radar and IR, so it's not like a plane is either stealth or not. It's the question who could detect, locate identify it with what effort.
Modern Radar (like the on in the F-22) is very well capable of tracking an object like the F-35 over hundreds of kilometers. The F-22 is not so easy to detect, but far from invisible.
Given the rapid advances in semiconductor and software tech. it's only a matter of a small number of years time until the chineese (e.g.) will be able to control larger airspaces for planes like the F-35 and probably the F-22.
EF and Rafale are much easier to detect (somewhat stealtheir then an F-18 - depending on the angle or typ of radar)
Therefore it's discussed that the F-22 and the F-35 will have to be replaced in many mission profiles by UAVs which can be designed even stealthier and don't mean the loss of an (expensively trained) pilot.
F-35s apeal is it modularity, maintainablity and total cost of ownership. Nations will buy it because the folks on the buyers list where promised work packages in engineering and production. A multicultural fighter so to say.
.....do you have Elven wizards deployed that can throw fireballs?
America does.
The F-22, or any other plane for that matter, doesn't have to be able to out run it's target. The question is can the target out run the F-22s missles, or guns? Which leads us to a second point.
The F-22 is not so easy to detect, but far from invisible.
It doesn't have to remain invisible all the time, just long enough to get into a good firing position; which it appears to be very good at.
Not saying planes aren't good. Just making the point that the F-22 has raised the bar, and unless some putz steals or gives the technology away the F-22 will be at the top of the food chain for a while...IMHO.