I would suggest that you go for MS in Stats. A good foundation of machine learning comprises of mathematics, statistics and computer science. A graduate degree in statistics should equip you in the first two fields by providing a systematic and in-depth education in those fields. As far as computer science is concerned, most of its education takes place online anyway so you can learn (or rather pick up) anything you want from the internet itself.
Further, in terms of employability - there's far more software engineers than applied statisticians who can code. If you're serious about working in machine learning, as a statistician with a theoretical and practical understanding of ML, you'll be far more in demand and far less replaceable. (Not that software engineers have poor employment prospects, but assuming we're talking exclusively ML heavy roles here).
Remember that the market has two sides, however. There are many software engineers because companies need more software engineers. Also note that a CS program gives you flexibility in learning to code and specializing in ML/statistics.
