I would definitely have won that bet. The North polar region consists if ice floating on the arctic ocean, whereas Antarctica is a continent covered by ice. The ice partially melts in the arctic ocean, but never melts in the South polar region. It has not always been thus, but you have to go back scores of millions of years.
That's always been the case. The Arctic is a liquid ocean while Antarctica is a solid frozen continent. It's like ice water in the fridge vs. ice in the freezer.