What are the advantages and disadvantages of each?

From what I've seen, either one can work as a replacement for the other if need be, so should I bother using both or should I stick to just one of them?

Will the style of the program influence my choice? I am doing some machine learning using numpy, so there are indeed lots of matrices, but also lots of vectors (arrays).

As per the official documents, it's not anymore advisable to use matrix class since it will be removed in the future.

https://numpy.org/doc/stable/reference/generated/numpy.matrix.html

As other answers already state that you can achieve all the operations with NumPy arrays.