Here is the best reference I could find online for the Harrier's air-to-air capability. I'm going to have to do some more digging to find references to the Decaminnou (sp?) flight exercises, similar to Top Gun, where the Harrier beat out the F18 and F14 aircraft at ratios between 5:1 and 8:1. That is saying a lot, because the F14 was designed to shoot down six fighter-bomber aircraft for every one of its own that gets shot down, and it lost to the Harrier at a 5 or 6 to 1 ratio. Keep in mind that the Harrier was DESIGNED as a CAS fighter-bomber, not necessarily as an air superiority fighter. That's kind of like saying that this van I drive is fast enough to beat your Ferrari in the 1/4 mile 5 out of 6 times on the line.
After reading this reference below, I think it's a pretty good article, so I'm going to post it afterwards in its entirety.
http://www.airpower.maxwell.af.mil/airchronicles/aureview/1985/jan-feb/bingham.html
Besides its air-to-ground capabilities, the AV-8B's air-to-air potential is greater than many observers have realized. According to B. R. A. Burns, Chief Aerodynamicist at British Aerospace Aircraft Group, in other than beyond-visual-range (BVR) air-to-air engagements, maximum speed is often less important than maneuverability and the ability to change energy by accelerating or climbing rapidly. He points out that, particularly with modern missiles, there is no escape from close air combat by speed alone; once engaged, only superior maneuverability or tactics will win the day. Except for "slashing attacks on an unwary foe, speed is an embarrassment because rate of turn is restricted by G limits (structural or physiological)." Burns identifies three key parameters for achieving success in air-to-air close combat: maximum sustained (thrust-limited) turn rate, maximum attained (lift-limited) turn rate, and specific excess power.9 The AV-8B performs extremely well in all three of these areas.
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The AV-8B's vectoring in forward flight (VIFF) and high thrust-to-weight engine permits agile maneuvering. Also contributing to make the AV-8B a formidable air-to-air opponent are the aircraft's small size, smokeless engine, raised cockpit, electronic countermeasures, AIM-9, and cannon capability. Finally, as the manufacturer points out, composite materials and emphasis on reliability and maintainability have significantly reduced the amount of maintenance support that an AV-8B requires.10
The increased operational flexibility gained from V/STOL capability has still another potential advantage. As the Falklands/Malvinas campaign demonstrated, RAF Harrier pilots without previous special training were able to operate from ships. Thus, a V/STOL force could make feasible far greater interservice cooperation in both aircraft procurement and operations. For example, if, during a future conflict, sufficient aerial refueling assets or en route CTOL air bases were not available for ferrying Air Force tactical aircraft to a distant theater, V/STOL aircraft could use ships equipped with the Arapaho system, not necessarily large-deck aircraft carriers, to reach the theater. In the Arapaho program, the Naval Air Systems Command has developed a portable, modularized aviation facility intended for installation aboard container ships. It can be installed in less than twenty-four hours and includes all components necessary for V/STOL aircraft operations: flight deck, hangar, fuel, and crew accommodations. It is estimated to cost less than $20 million per set.19