Flanker and Eagle - Dogfight!
In all likelihood, neither aircraft will maneuver to escape, because each would still be within the other's missile envelope. They will both evade the onrushing missiles while trying to maneuver closer for another shot. The F-15 would rely on its electronic countermeasures and speed to get away by flying higher and faster away from the missile, and the SU-27 would use its maneuverability to turn tightly and throw off the AMRAAM.
Assuming both fighters evade, they would likely return to closing head on, with the Eagle slightly higher and moving at greater speed than the Flanker.
The SU-27, due to its helmet mounted HUD can attempt an off-boresight infrared missile shot as the fighters approached. IR missiles are less accurate when fired in this manner but this would at least disrupt the F-15's approach.
The Eagle will probably overshoot the Flanker while evading, but as the F-15 has an acceleration advantage, it could try to keep the fight vertically oriented, looping high and work behind the Flanker. The SU-27 will probably try to remain in the horizontal plane, utilizing its superior turning radius to go for another off-boresight missile shot using the helmet mounted HUD. A stalemate would well ensue at this juncture where the Flanker continually turns inside the Eagle, but is unable to get off a shot while the Eagle maintains a speed and height advantage, unable to keep its nose on the SU-27
In all likelihood, such a battle would end when one pilot made a mistake. One thing is certain - the Flanker could possibly survive one mistake if it led to only the 20mm rounds from the F-15's internal Gatling striking it, because titanium is a very difficult substance to penetrate. The Eagle would not survive a hit from the Flanker's cannon - 30mm rounds would shred the F-15.