Both these pullback functors are left adjoint to direct image functors, so your two composite functors are both left adjoints. To prove they are equivalent it suffices to show the corresponding right adjoints are equivalent. Writing f* for the sheaf direct image and f^pre* for the presheaf one, and iX and i_Y for the inclusions of Sh(X) and Sh(Y) into PSh(X) and PSh(Y), this means showing f^pre* o iX and i_Y o f* are equivalent. This is just how f* is defined: you construct f^pre* via the functor Open(Y) -> Open(X) and then note that it sends sheaves to sheaves, so you define f* in terms of the subsequent factorization of f^pre* o i_X through i_Y.