I'd have to go with my gut, since indeed, some hard soldiers may be more likely to stick around if they have a chance of winning, but they may also be more likely to flee if they are going to die. Also, motiviation comes into play. Mercenaries who maybe aren't getting their biggest paycheck of the year aren't going to fight you to the death, mercenaries promised a billion GP might. Zealots may never flee. Bushwhackers will flee in an instant so they can come back to hit you again.
In short, it seems much to complicated to come down to a dice roll.
Though, I could see great use for a fear RR (especially if your party isn't a bunch of grizzled veterans) in hairy combat situations.