Honestly, either is fine. It depends on your learning style and priorities. If you want to jump quickly to getting state of the art results with rich datasets like images and natural language text, then start with the deep learning course. If you want to get a deeper understanding of feature engineering, model interpretation, and (especially) techniques for tabular data, start with the machine learning course.

Also, the machine learning course was originally the initial introduction for a masters program, so it is a little less intensive and fast moving. But it also assumes a little more math background in parts, since everyone in the program already was pretty familiar with linear algebra, probability, and statistics.

In the end, the two courses go together pretty well, so I don't think it matters too much what order you do them in.