Against stealth aircraft, it depends entirely on the nature of the battlefield. If the USA attacks another tiny, defenceless country again like Iraq (lets say at random North Korea) then they will have superior numbers, AWACS support and a massive advantage in intelligence (satellites watching airfields etc.).

Stealth aircraft such as the F-22 will no dooubt have an even clearer advantage over Mig-21's with their old radars. It would take a miracle for a Mig-21 pilot facing an enemy of that scale to get a shot off. For example if an F-22 pilot forgot to look at his monitor and got behind an aircraft to shoot it down, without realising there was another aircraft behind that one (and therefore behind him).

However in a super power war things are different. AWACS aren't a guaranteed resource and Russia has some of the best anti AWACS weaponry in the world. They have 600km range super long range anti-radar missiles that can be launched from the Mig-31. Their 4th generation aircraft are superior to the USA's 4th generation aircraft, due to being built in response (10 years later). So unless the stealth fighters make a huge impact early on, they are going to find themselves without backup and being forced to use their search radars.

Now in the early stages, these aircraft are going to go for Russian AWACS. They will have to fly through throngs of Russian aircraft, which are superior at WVR combat. Their missile range is 48km which means they will probably have to take out Russian fighters before they get there. If a US AWACS approaches close enough to support them it will be shot down by Mig-31's (with greater range then the AWACS radar). So they will need to use their search radars, which makes them visible to any aircraft within 300km, albiet briefly. This makes their mission very hard. If they turn it on to find 4 Su-27's flying only 100km away they may instantly have up to 20 missiles incoming. If they turn it on to find a Mig-29 patrolling 10 km in front, they will have an agile dogfighter coming in with perhaps 100 aircraft supporting him by firing barrages of long range missiles.