By integrating constructs from the λλ-calculus and the ππ-calculus, in higher-order process calculi exchanged values may contain processes. This paper studies the relative expressiveness of HOπHOπ, the higher-order ππ-calculus in which communications are governed by session types. Our main discovery is that HOHO, a subcalculus of HOπHOπ which lacks name-passing and recursion, can serve as a new core calculus for session-typed higher-order concurrency. By exploring a new bisimulation for HOHO, we show that HOHO can encode HOπHOπ fully abstractly (up to typed contextual equivalence) more precisely and efficiently than the first-order session ππ-calculus (ππ). Overall, under session types, HOπHOπ, HOHO, and ππ are equally expressive; however, HOπHOπ and HOHO are more tightly related than HOπHOπ and ππ.