They cannot be both false (for other reasons).
Assuming both are false, there isn't $1mil in either of the boxes, and according to the sign on box B, box A doesn't contain a snake - but each box has either or, hence it's a contradiction, and we were wrong in our assumption.
So both are true.
edit: These riddles remind me that they should still release at least the second in the Professor Layton series :/
Maybe the question should have been "Would you open a box at all, and if so, which", would make it trickier.