Actually, the choices aren’t limited to XX or XY. There are several other possibilities, each of which appear in anywhere from 1/5000 to 1/500 of the population (about 1 in 300 people may have one of the abnormal combinations). These include: XO, XXX, XXY, and XYY.
http://anthro.palomar.edu/abnormal/abnormal_5.htm
But those rarer chromosome combinations are still always the same gender. XO is only females (Turner’s syndrome). XXX is always female. XXY is always male. XYY is always male.