The only aircraft that has any advantage in any area would be the Russia Mig-31. It can fly faster so if used correctly it would have the best chance at getting a kill against the F-22.
If the radar is big enough you can detect a stealth plane. Stealth only reduces the range it can be detected. If you reduce the radar cross section to as small as 1% of an unstealth aircraft it does not mean you will detect it at 1 mile opposed to 100 miles away.
The Mig-31 has a big nose and with a powerful radar it may very well detect an F-22 at beyond visual range. If the Mig-31 did detect an F-22 its safe to say that it would be because the F-22 had just launched a missile. The Mig-31 may be able to get a lock and fire off a missile before it gets shot down.
Its not quite that simple. The kinematics of the F-22 would seriously challenge any conventional BVR missile even if it could lock on. Moreover, the missile seeker itself would have to be able to lock on during the terminal phase and by definition missile seekers are small. Not only that, the SA advantage of the F-22 would allow it to dictate the terms of an engagement.
-DA