Which way to travel between Alice Springs and Darwin?

I'm going travelling with a friend later in the year, and we have our route of australia mapped out apart from one section. Between Alice Springs and Darwin we are not sure whether to go from North to South or South to North. We have a two week gap for the two areas and are looking to spend about a week in both. I noticed that December (when we will be there) is part of Darwins rainy season so im not sure if that will have a bearing or not. Any help from locals or travellers who have done this before would be greatly appreciated.