It is nice when an expert on subjects like this (Eagl) shows up and actually puts fact into the discussion. The actual facts you can learn are so much nicer than the opinions that abound.
It took me a while to post after I saw this thread, mostly because I can't share the most relevant or convincing analysis. Every aircraft has limitations, and the exploitable tactical ramifications of those limitations are not always obvious or trivial.
Armed only with the gun, I would not want to take anything but an F-22 up against a gun-only flanker variant. With full-up systems, no tactical handcuffs, and reasonably even number of opponents though, I'll take any Eagle variant including a heavy/draggy F-15E.
It should be noted that NASA and Boeing (MacD) experimented with modifying the F-15 with canards and vectored thrust nozzles. It gave the plane similar extreme maneuvering capabilities as the flanker, but the cost wasn't worth the minor edge it would give us in the limited close-in dogfight scenarios. Plus the mod would add weight/complexity, increase fuel burn, decrease top speed, etc, basically reduce the overall ability of the F-15 to be the worlds best all-around air dominance fighter.