That "disdain" was a bit of the First Doctor that Davison wanted to instill. It really wasn't uncommon for the Fifth Doctor get cross with his companions--he even once called Adric a "young idiot" to his face. I don't think it was so much that as Davison thought Nyssa was more of a "traditional" companion (at the time). Pretty much there to be deferential to the Doctor and not challenge & question him like Tegan often did.
Tom Baker for the win... Turlough is the one I didn't take a shining to, though Mark Strickson has gotten more handsome over the years.