Daishi: You do NOT want to pull a Kobra in mid-dogfight. You do that, your ass is grass. Any experienced fighter pilot can loop over and nail you, cause you can't maneuver at all (the Kobra has to be performed below either 450 or 250 knotts, I forget).
Also, the Su-37 can not out-maneuver a long-range missle as well as you think. Those suckers are fast. If it's launched head on, pow, you can barely maneuver, launched from the rear, pow the missle can follow you anywhere. Close range in, tho, the Su-37 does have a significant advantage with it's high and low speed maneuverablility, and it's helmet-mounted missle sight (Su-37 does have a helmet-mounted site, correct?), which can launch a missle at a target up to 45 degrees off the nose. However, using the superior balance of thrust/weight ratio and turning ability, the F-22 does have the ability to come out on top. And with the new helmet-mounted sight on the F-22, the playing field will be equal in that respect. The F-22 also has better avionics, many Russian aircraft are built to old-time USSR tactical doctrine, i.e. pilot making very little decisisions, so the equipment onboard is far less advanced.
However, I'm NOT saying that the Su-37 couldn't beat a F-22. In fact, they're quite evenly matched, it really all comes down to the skill of the pilot. I'd rather fight a really dumb-ass pilot in an F-22 than fight a really experienced pilot in, say, an "old" F-4 Phantom.
EDIT: Herz, you know that the standard engine for the Mig-29 only has 400 hours of service life? Try that for toughness, lol, compared to the 400,000 or so of the F-16s engine before it needs an overhaul.
But, yea, some Russian birds are really tough, probably tougher than many US jets.