The Russian "Flanker" SU-27 aircraft can do those maneuvers without canards and without thrust vectoring nozzles. Not as easily as the newer SU30-MK/MKI aircraft but they can still do it. They allow a lot higher angle of attack, in fact the pilot must override the flight computer to allow such high angle-of-attack to do something like the "Pugachev Cobra" (search video on that
). The Mig-29 can do most as well. Keep in mind a lot of these aircraft have crashed doing these little tricks.
Adding the canards and the 3D Thrust Vectoring (TV) to the Russian aircraft (and India - China does not have the TV engines - yet) can give a skilled pilot a lot of advantage in a furball with our pilots.
US aircraft do not have that similar combination of canards, 3D TV nozzels. The just reaching squadron service F-22 Raptor has "2D" (up and down) thrust vectoring and they feel that it is all that it needs. The F-35 JSF (not yet in production) does not have thrust vectoring. The F15 has decent juice but no TV and not quite the cornering of the Flankers. The F16 is great at fighting in a one circle fight and turns well at higher speeds and higher altitudes, the F18 likes to fight low and slow. One Navy F18 pilot I saw in an interview said no fighter he has ever flow gets slower faster than an F18 and no fighter takes longer to get faster again (good and not so good). All planes have particular strengths that you want to make the other guy fight you fight and not his.
The F-22 can do some of the tricks that a Flanker can do a few of its own, and there is that little stealth feature and also supercruise (flying faster than sound without afterburner). The F35 is supposedly low stealth meaning stealthy head on but not as much as the F22 from other angles...
In a one on one "guns" dog fight with similarly skilled pilots the Flanker will
possibly win more engagements due to a more maneuverable aircraft. In shorter range missile engagements within visual range the Russian missile can supposedly be launched well off bore site, almost over the shoulder (60-80 degrees off center in either direction) and track its target as the pilot wears a helmet mounted site. The US has some of this capability with the AIM-9X sidewinder but that isn't as available.
As for the Flanker making all those turns that the F15/F16/F18 can't and the theoretical use of the "cobra" and a missile launch does have one big glaring problem for the Russian (Chinese, Indian, Venezuelan, Malaysian, whoever) he's dead by the other guys wingman because while he may have gotten one of his targets he is now dead in the air with little or no airspeed because those manuevers only happen at lower speeds <300KTS and brings his speed down so quick where he needs to gain speed and energy again to do much of anything.
Others argue that if you've gotten so close to a Flanker that you are in a knife fight that you've screwed up.
I'll try to dig up a couple videos... Otherwise Youtube Pugachev Cobra
I'm not a fighter pilot but I play one on PC
I really 
enjoyed
the ride
Linear Mode
