In all 5 campaigns I've played so far, the HRE is crushed quite early. So my vote goes to the HRE.
Russia, Hungary and Milan do most of the time very well, as does Egypt after the Mongols show up.
The Mongols have *never* gone after Russia, they've always gone after the Turks and Byz, moving into Europe.

I think the Mongols just come to the player faction at the shortes possible route.
I'll have to start another game as the Russians, I think...