It was conjectured by Halpern and Kapron (Annals of Pure and Applied Logic, vol. 69, 1994) that frame satisfiability of propositional modal formulas is incomparable in expressive power to both $\Sigma^1_1$ (Ackermann) and $\Sigma^1_1$ (Bernays-Schonfinkel). We prove this conjecture. Our results imply that $\Sigma^1_1$ (Ackermann) and $\Sigma^1_1$ (Bernays-Schonfinkel) are incomparable in expressive power, already on finite graphs. Moreover, we show that on ordered finite graphs, i.e., finite graphs with a successor, $\Sigma^1_1$ (Bernays-Schonfinkel) is strictly more expressive than $\Sigma^1_1$ (Ackermann).