If we list the possible combinations before we're told anything, and listing the eldest child first we have 4 possible outcomes:
Since I have two children, and we know that at least one is a boy, there are three equally probable cases: Boy-Boy, Boy-Girl or Girl-Boy. In only one case are both children boys, so the probability that both are boys is 1 in 3.
My sister's situation is different. Knowing that the older child is a girl, there are only two equally probable cases: Girl-Girl or Girl-Boy. Therefore the probability that both children are girls is 1 in 2.