I never tried to play COE3 in MP, it sucks for me royally as a single player game.
Interestingly enough, it suffers from the same problems as FE, namely problems of scale. It tries to be a kingdom/empire simulator without giving you the means to do so. You have to wait years to hire pitiful five ragtags with pointy sticks, yet the game constantly spams ridiculous monster stacks like rabbits, snakes, deers and whatnot that are capable of capturing villages, even castles. What rubbish. Combat is silly and obsolete, because the defender always strikes first, so with larger armies, attacker suffers insane losses without means to do anything about it. Men at arms have the same armor as naked madmen, namely 0. Magic is random and casters use nonsense spells in combat all the time.
The game fails to abstract menial tasks, so most of the time you spend hours trudging through empty landscape with a band of underfed invalids, only to find out "OMG, dragon, not this way, run AWAYYYY".
You can't manage your kingdom in a meaningful way, you can't build defenses, you can't scout, you can't conduct diplomacy. You are constantly waiting for something. There are minimum amount of meaningful choices. Important events are very much dependent on random encounters.
The AI is dumb as rock, it follows no strategic plan, and it cannot play without INSANE cheating bonuses even on moderate levels.
The game could be a hit, though. In 1985.