Some of my old posts on the subject might still be in the forums, if you search back far enough...
For this discussion though, it isn't too tough to summarize. Equal pilots, 1 vs. 1., in a close-in guns only fight, a flanker has a great chance of getting the first shot from a position of advantage most of the time. It has both enough slow speed maneuverability and thrust/weight to be able to get and keep an F-15 defensive yet unable to run away. An F-18 has great low speed maneuverability, but it doesn't have the thrust/weight to keep the temporary advantage it can gain with it's high angle of attack capability. The flanker has both.
Throw missiles or even a slightly more complicated scenario in there however, and the systems integration of even the "old" F-15Cs may be decisive. The aim-9X, amraam, and even old aim-7, combined with either the old or new AESA radar, plus the new helmet mounted sight, is utterly lethal because it means that if the eagle driver can *see* the opponent either visually or with the worlds best air to air radar, the opponent is dead dead dead. The joke about "wish them dead" weapons is pretty darn accurate when you consider the new off-boresight capabilities the eagle has.
Not saying that the flanker and all of the fielded missiles available for it are not good either, but on balance I think the eagle is still easier to fly and employ which means faster detection, targeting, and weapons employment with a high Pk. And the real world scenario is never a simple as 1 vs. 1 (or even 2 vs. 2), which means the time from detect to shoot gets delayed. Again however, that is where the F-15 systems are still outstanding. Still, the more recent SU-27 variants are getting better and better, and an F-15 without support is still just an old fighter with good missiles. Which is why it is long past time to replace the F-15. Maybe someday the USAF get an F-15 replacement but that isn't looking very likely for the forseeable future.
And of course the caveat is still don't get into a knife fight with a flanker because he'll turn up his own bunghole and shoot you before you know what happened. The best bet even if you have to do a visual ID is to sneak up unobserved or deny him a shot (classic out of the sun sort of stuff) until you get close enough to see him, get your ID, then run away bravely while your wingman takes him out with an amraam as soon as you are far enough separated to not get fragged.