L&S,
At the risk of repeating others, my four penn'orth, based purely on my interpretation of the historical examples (former victims of Air SCP, Swindonshire, groan inwardly and ignore the rest of this posting).
Your question is a good 'un. I think you've probably found out, though, that the answer usually can't be found in a single factor: for manoeuvre alone to be the decisive factor is rare. It presupposes that we take two fighter pilots of absolutely equal quality - ranging from experience, training, ability, getting out of the right side of bed, not having momentary brain fade that passes the advantage to the opponent, etc - in aircraft with similar weapons systems (i.e. visual range only), with similar fuel states so neither's thinking 'time to go home...'
Then, if all these improbable criteria are met, having your MiG-29 against an F-4, let's say, means one successful MiG pilot. As I'm certain you've discovered, examples of this are rare. I'd contend that the whole point of manouevre is that it gives the pilot of the more manoeuvrable aircraft an advantage. This may be the ability to disengage rather than press home the fight.
Tweo examples: 1917, Royal Naval Air Service Sopwith Triplanes versus Albatros series. The manoeuvrability of the Triplane enabled RNAS units to gain an advantage. When the RFC/RNAS had aircraft (e.g. FE8, BE 12) which were easily outmanoeuvred, the German Air Service gained air superiority. When the Triplane, followed by the Camel and SE 5a came along, their enhanced power of manoeuvre - amongst other things - altered the balance. In the case of the Camel and the Triplane, manoeuvre was arguably the key factor. That said, the dear old Red Baron et al were still able to rely on skill, cunning, experience, training, tactics, etc to make a fight of it.
Battle of Britain (sorry). Hurricane/Spit vs. Me109 can be debated for ages - but my view is the Hurri/Spit vs. Me110 is the better illustration. Goering (never the greatest judge) thought that the 110 would clear the skies - but, despite heavy armament, good pilots, etc, it didn't. The manoeuvre capability of the Hurri and Spit meant that it was at a disadvantage; given the Luftwaffe force structure, so was the Luftwaffe. Although not fighter v fighter, argubaly the most accurate bomber in the German arsenal, the Stuka, was withdrawn because it was slaughtered by more manoeuvrable aircraft.
OK, a word on the 109 - again, I'd argue that manouevre was a factor. The Hurricane was largely disadvantaged, but a case could be made to say that its ability to out-turn the 109, and thereby stand a chance of surviving was important. This was more so with the Spitfire. Not overwhelming decisive factors in the campaign, but important contributors, I'd say.
Post WW2, with BVR, IR, and a whole host of clever devices, the question isn't easy to answer. BEagle's right, though. The F3 was designed to splash bombers. The fancy manoeuvring on the central front would be done by USAFE F-15s, a whole array of F-16s and...er... 19 and 92 with FGR 2s.
It comes down, I think, to two points:
1. In certain circumstances, having the power to outmanoeuvre an opponent within visual range can offer an advantage. Since 'there are no prizes for coming second' (or other suitable axiom/cliche), it's worthwhile having enhanced power of manoeuvre.
2. Given that we can never be certain that zapping the enemy from BVR will be in the ROE, it helps to have the advantage described in (1).
But overall, I would contend that the record shows manoeuvre to be one of the 'have to have' features for any aircraft meant to go head to head with enemy fighters, even if, in practice, that quality is not often used. The factors of pilot quality, weapons systems superiority and so on can negate it, and there is much evidence of this (Vietnam, etc). But why risk it and not have it? The USN would have ended up with the F-111B or even the straight-winged F6D Missiler, which wouldn't have cut it over the Gulf of Sirte...
Many, many apologies for the length of the post.