My knee-jerk answer was "X and Y," and on further reflection that seems the logical answer, too. There is a universe of two outcomes -- conjunctive, not disjunctive -- and we must choose the greater of those two. But for many people, "the greater of X or Y" sounds right.
What's the answer, and what's the rule?
I don't know the rule, but I know the answer. Rewrite the damn clause so that it requires "the payment of X or Y, whichever is greater."