Dnil,
To my knowledge Russians didn't use first class technology in cheznya.
Besides the wars against guerrilla forces are very different from the conventional wars between armies.
Like some might've noticed some examples of it in the recent Iraq war, although nothing comparable to afganistan or cheznya.
People were far more motivated against russians than americans in Iraq - where Iraq's own armies fled from saddams rule :>
If you want an example how it works against US, just look at the Vietnam war - how much good did the US technology do there?
There was a blend of guerrilla war and typical war armies vs armies.
Russians do have some impressive systems designed, that US doesn't, but does the goverment have money and will to utilize it to an extent that US does?
So far russian stuff has been more into simplificy (reliability) and lesser prices.
Where as US does everything opposed to that :>