It won't start WWIII, that's for sure. It may up the amount of support that Russia gives Serbia, but it will be interesting to see the international reaction to a NATO attack on Russian peacekeepers. The Yugoslav Wars may be seen more as a proxy war in popular consciousness than an internal conflict.
In regards to the actual action, I doubt it would be much more than a skirmish. The Russian paratroopers of the time would've been of far superior quality to the NATO troops. Assuming no air support is called in (we can safely assume that, because NATO wouldn't want escalation, just to discourage the Russians from supporting the Serbs), then the paratroopers will probably win, outnumbering the NATO troops 2:1, with better training, AND in a defensive position. The Russians lack heavy weapons, but the NATO forces wont want to raze Pristina airport, just capture it and disarm the Russians. I doubt that the Russians would have no anti-armour capability, so my money is on an initial skirmish, indecisive Russian victory, followed by bi-lateral political negotiations.