This is for you, LFN.
At first I thought this thread said, "Princing the Prizes".
So generally I think Princing Prizes is not going to be a thing, since it involves having already bought Tournament and Province, and succesfully collided them, and then spending another $8 on Prince at some point, and having *that* collide with the Prize (or maybe you Butchered your Province into a Prince - interesting ...). By which time, your opponent has grabbed two Prizes of her own and moved onto emptying the Provinces. However, which Prizes are worth Princing should you get the opportunity?
Diadem, obviously not.
Followers, almost certainly, and that's going to make the game crazily quick after that point.
Trusty Steed, also almost certainly. It would probably also be the one time its Silver gaining could be fast enough to make for a decent Feodum strategy.
Princess, yes unless you're trying some tricksy TfB strategy.
Bag of Gold ... eh? Maybe not so much, since your engine already has a decent source of cash if you've gotten this far, so Golds probably aren't so great unless they're TfB fodder.
So the order of preference for Princing Prizes probably primarily preserves the preferred permutation (sorry, once I got to "Princing Prizes" I knew I had to keep going).