Two finite rooted frames are isomorphic iff they validate the same formulas.
(This is an exercise in the book "Modal Logic" by A.Chagrov and M.Zakharyaschev)
The key-phrase here is `Jankov-Fine formulas'. See Theorem 95 and Exercise 98 here: http://www.illc.uva.nl/Research/Reports/PP-2006-25.text.pdf. So, by Theorem 95, if $F$ and $G$ are finite rooted frames which validate the same formulas, each of them is a $p$-morphic image of a generated subframe of the the other. By Exercise 98, this implies that they are isomorphic.