Assume so since it’s newer, would it win easily?
I might be wrong. But I don’t think modern fighters are designed for dog fighting. Just sit back, get a missile lock and fire.
If the Tomcat could get a lock with its Phoenix missiles. the F-22 is toast. its ability to do this is, of course, classified.
The F-22 wouldn’t win because it’s newer. It would win because it has better engines, better maneuverability, better weapons, better avionics, is harder to see for targeting purposes …
The F-22 is the new air superiority fighter, designed a good 35+ years after the F-14, whose original mission was an interceptor.
If you’re going to match fighters, think more in terms of the newer F-18 versus the F-22. The F-22 would still win in the hands of a sufficiently skilled pilot.
I saw a show on the discovery or somesuch channel about the F-22 testing against some other jets. The Raptor was taking them out like 4 on 1 with no trouble. The other jets never even saw the Raptor before they were dead.
The Raptor is a stealth aircraft, has much better electronics and is simply the superior aircraft. Its not even a contest.
This is a goal of defense contractors and the military infrastructure but does not apply to the F-22. Many have speculated that the F-22 and the JSF will comprise the final generation of manned combat aircraft. Still, it’s incorrect to say that the Raptor has any directly to do with this premise, at least no more correct than saying the F-15 or any previous fighter was a step towards that goal. The concepts are distinct from on another.
I remember this story. The Raptor pilot felt kind of sorry for the opposing pilots. The raptor always wins without any trouble even at high odds (4 to 6 to 1). (according to the military pilot. That might be disinformation, but I believe the pilot. Technology has increased a lot from the early seventies (F-14 F-15 design era) to the early nineties (F-22 design era).)
In a November 2005 test mission, 4 F-22 fighters were able to defeat 33 F-15C fighters in mock combat without a single loss. The only advantage the Tomcat has over the F-22 is the long range Phoenix missles, but given the stealth built into the F-22, the F-14 would have an very difficult time getting a lock.
It doesn’t mention either the raptor or the tomcat, but may be of interest anyway…
I believe the word you’re looking for is “graduakkily”. 
The F-22 is impressive, but these mock dogfights need to be taken with a carton of salt. When funding is tight, the world’s militaries tend to stack these confrontations, for the best showing possible, however theoretical. Witness the high-altitude missile defense system and numerous other early systems, some since halted.
We have a plane that turns into toast when attacked? COOL!
… and speaking of cartons of salt, that is also what we should apply to the claims of capabilities of accuracy and range regarding the F14’s Phoenix missile.
I don’t mean to rain on anyone’s parade, but the Phoenix missile was retired over a year ago, and the F-14 is being phased out in favor of the F-18. Not so much because of the weapon system’s age (though that is a factor), but because it’s mission has become obsolete. It was designed to knock down large, high-flying Soviet nuclear bombers before they can get close enough to attack a carrier task force. That threat no longer exists. Also, current military rules of engagement mean the Phoenix would never have been fired out to maximum range anyway and there are more effective weapons at those ranges where the missiles would be allowed to be employed.