In the absence of a worldwide warming trend, there is a large scale oscillation, the thermal bipolar see-saw. When the arcticArctic cools, the antarcticAntarctic warms and vice versa. With a worldwide warming trend, even if both are warming, the oscillation will still cause one to race ahead of the other, then switch places.
See the article https://www.nature.com/articles/ngeo1026Expression of the bipolar see-saw in Antarctic climate records during the last deglaciation.
Other differences besides those mentioned in other answers:
- Due to weird chemistry, increasing CO2 over Antarctica causes a reverse greenhouse effect - it cools the surface! See the article https://www.nature.com/articles/s41612-018-0031-yUnmasking the negative greenhouse effect over the Antarctic Plateau.
- There is a lot of vulcanism under Antarctica. We don't know how much melting to attribute to that.