I know most organisms are moving towards the poles due to climate change. Does anybody know if they are moving faster in the north or south hemisphere and why?

Well it really depends on the species and the types of land use. Species (both plants and animals) move most effectively when there is an unbroken corridor of suitable habitat. Unfortunately, extensive human land uses such as agriculture, roads, and urban development can often cut off essential corridors for migration, effectively preventing organisms from moving in the patterns they otherwise would.

My guess is that areas with long North-South stretches of undisturbed landscape would facilitate faster species migrations. Typically, these corridors often end up on mountain ranges, such as the Appalachians in North America, or the Andes in South America, as mountainous terrain is simply more difficult for humans to traverse and develop.

But it also depends on the species. Many birds for example don’t care much about terrain and will simply migrate to suitable habitat patches rather quickly. A small forest herb on the other hand can only disperse its seeds a few meters each year on average, and can only grow in the deep shade of an undisturbed forest, meaning it needs unbroken forest to migrate and will take a very long time doing so.