Machine with an oracle for a language that cannot decide another language in polynomial time
Let $A,B$ be two incomparable Turing degrees (these can be constructed by diagonalization, known in this context as forcing). If $P^A \subseteq P^B$ then in particular $A \in P^B$, and so $A$ reduces to $B$; since we know this is impossible, we can conclude that $P^A \nsubseteq P^B$. Similarly $P^A \nsupseteq P^B$.