There is no Prince John in Prince of Thieves, but the Sheriff is essentially that role. He machinates for the throne and is the primary antagonist.
I’m quite sure that Alan Rickman knew exactly what he was playing, but I’m sure I don’t. As I mentioned before, he’s in a different movie from the rest of the cast. He’s delivering large: big expressions, dynamic voice, comic reactions. It’s more of a stage than screen performance.
I would say he’s driven by envy, like the other Prince Johns, but he’s not brother to the king. Who does he envy? He has a wooden statue, life-sized, made of himself. He’s possibly just envious of anyone who has society’s attention.
He puts his trust in a witch woman. She has a satanic altar? I don’t know. She’s almost a freaking Muppet she’s so strange and inexplicable. Is she his mother? Look, don’t try to understand. He’s superstitious, though, and she’s basically one of the spinners of fate to him.
And he wants Marian. She’s the only eligible woman in the movie, so who else would he want? Did he desire her before Robin started paying attention? I can’t remember. At the climax of the movie, though, he tries to impregnate her on the floor, wrestling about in a semi-rape, semi-slapstick way, as the priest who married them is still standing there. I swear, the scene is possibly the worst Eight ever filmed. He does fight Robin and end up dead, though.
He’s emotional, he’s funny, he’s envious, and he’s only marginally competent at fighting. Four. Like Robin’s character, I believe he played the trope rather than the script, but he was consistent.