As you remember, the Arctic is an ocean surrounded almost entirely by land. For this reason, the sea ice that forms there is trapped and does not move around much. It moves a bit through the cold Arctic waters, but that's it.
Conversely, Antarctica is surrounded by only ocean. This lack of obstruction allows the sea ice that forms there to flow and move, often into warmer waters where it will melt.
Due to its ability to flow away and melt, nearly all Antarctic sea ice that forms in the winter melts in the summer. This results in thinner sea ice in Antarctica in general, as most of it is single-year ice.
In the Arctic, the sea ice that gets trapped by land does not melt, and some remains through the summer, continuing to grow when autumn begins. This results in thicker sea ice, as much of it is multi-year ice.
There are differences as well in the snow cover of sea ice. The Arctic, being covered with ice and surrounded by land, does not get much precipitation, and therefore does not have much snow on top of its sea ice.
Antarctica, being surrounded by water, has greater precipitation levels and therefore has sea ice that has a greater amount of snow cover.
