I think Prince was probably weirder. Much of Bowie's weirdness often came across as performative, but in interviews he frequently came across as a regular bloke 'cept with an art-school background... so he took many of those ideas seriously, without necessarily taking himself too seriously, or at least recognizing the absurdity of it all. Bowie appears to have had a self awareness which was missing from Prince.
THAT SAID... I don't know a whole lot about Prince, save for various magazine articles, one or two documentaries, and some of the press stories when he passed on. Never really got into his music. So I could be wrong.
Love Bowie. Never really cared for Prince.