I believe Russia has a jet that can outmaneuver the F-22 Raptor.
Maybe the Su-27 or the Su-37 are more maneuverable in a dogfight in close quarters (e.g. the "Cobra" maneuver) but our pilots are better trained and their planes aren't stealthy, if I'm not mistaken?
I'd say our guys still have the definite advantage--they could splash their target from miles away before the other side even knew they were there.
Oh hey, I just remembered--my cousin was an AF crew chief and told me a US pilot pulled a Cobra in an F-15 once... he was able to do it, but apparently popped a few rivets on the airframe from the stress.