As I've always understood it, a faction leader's dread works similarly to his acumen. Higher dread improves the loyalty of his provinces across the board, but it has a smaller overall effect than the dread of the local provincial governor. This reflects that the local lord is usually going to have more to do with keeping his population loyal than the monarch in some distant capital.

I pulled together some approximate calculations a while back, although I doubt they're very accurate -- they're based only on my general observations and educated guesswork as opposed to actual math (I'm just too lazy to bother ). For every point of dread a faction leader has, I believe it improves the loyalty in his provinces by ~2%, whereas a governor will improve loyalty in his specific province by ~8% for every point of dread he has.

To give an example: Let's say I'm looking at Castille, which is owned by the Spanish. Let's say that their king (Alfonso) has 4 dread, and that Castille's governor (Lord Santiago) has 5 dread. In this case, Lord Santiago would give Castille a loyalty boost of around 40%, while Alfonso gives it a loyalty boost of about 8%.

Note: Before anyone asks, I'm reasonably certain the faction leader's loyalty boost via his dread is not affected by the distance-from-the-king penalty suffered by provinces that are far away. That's a separate function, and does not directly interfere with the leader's dread ability. So in my above example, King Alfonso would still give all provinces an 8% loyalty boost, even if the Spanish occupy Novgorod on the opposite end of the map. Of course, Novgorod's loyalty will still suffer from the distance penalty, which will mostly likely negate most - if not all - of Alfonso's relatively meager dread boost. That 8% bonus is still there, however, even if it is virtually nullified by Alfonso not appearing in Novgorod in person.