Caligula wins this by a landslide. The man declared war on - wait for it - the sea, for crying out loud. Only a (self-proclaimed) god would do a thing like that.
I heard someone speculate Caligula did a lot of things with more intention behind it rather than being insane and that he was viewed as insane after death by people that hated him. Like putting a horse on a Senate seat? Maybe he was trying to say something about how much he valued the senators. Going to war with Neptune? Maybe the religious and gullible people really believed that?