Imagine a "grid" of people: some number of people arranged in a number of rows and columns in a rectangular formation.

We designate person A as the shortest person in the group of the tallest people of each row. We then designate person B as the tallest person in the group of shortest people in each column.

Who is taller, A or B?

Well....if the grid only consisted of two people on the same row. The shorter of the two would be person A. Naturally the tallest then would be person B.

Again if the grid only had 1 person (It would be square, which is a special kind of rectangle)person A and B would be the same person and so be the same height.

Therefore the answer seems to be variable.