Glad you asked, terminator....
The Su-37, admittingly, was a fascinating aircraft - digital fly-by-wire, 3-dimensional thrust vectoring, very powerful engines, and supermaneuverability. In my opinion, the Su-37 is the ultimate expression of the Su-27 Flanker line.
Yes, it could defeat the F-15 Eagle in a dogfight, but not by much. According to statistics I've read (can't remember the site), the Terminator's kill ratio against the Eagle is only 1.5 to 1, meaning for every 1 Terminator shot down, 1 1/2 Eagles would be shot down. Remember, the Eagle is still an extremely maneuverable dogfighter, despite its age.
But then the Terminator loses its advantage against the newer fighters, again according to statistics, it loses to the Eurofighter Typhoon 4-to-1, I believe the Gripen has a 2.5-to-1 advantage, the Rafale is dead even at 1-to-1 and the Raptor has an amazing 10-to-1 kill ratio advantage over the Terminator, pilots being equal in experience from every nation.
But unfortunately, this "ultimate expression" of the Su-27 Flanker line would find it very difficult to fight against the newer generation of fighters from Europe and the US.
Mig engineers claim the Mig 1.44 is better than the F-22 Raptor...so they say...it's only a claim, but that's what they said about the Mig-15 against the F-86F Saber. The Saber was definitely the better dogfighter, although the Mig was the better climber, but because of the experience of US pilots, they gained an 8-to-1 kill ratio over the Mig-15s.
The Soviets then, claimed they weren't flying those Migs, they were North Korean pilots... sure they were.