Master of Statistics or Master of Data Science
As everyone here knows, data science as a field is broad, and similarly the experience required for a particular job is broad. 

Depending on where you want to end up, either degree could suit you better. If you would like more of a traditional statistician's job which has been rebranded to data scientist in order to gain more attention, then perhaps the MSc Stats would be more applicable. However, if your field requires more complex computer programming or database management, you may want to look into the masters in data science or masters in computer science, depending on your background and interest. Going with a "hot" degree like data science means that you will likely learn a lot of common analyses in superficial detail in order to be employable quickly, but with a more traditionally academic MSc Stats or MSc Com sci, you will learn the theoretical basis with the potential loss of applicability. My personal bias is towards to academic side (MSc/PhD Stats or applied math), but I think this is a decision you should think hard about. Regardless of your decision, in general data science / analysis / programming / whatever this field is requires quite a lot of self directed learning, so whatever program you choose must provide you with the skills and tools to be able to teach yourself whatever you need to know.  

I would personally take a hard look at what specific kinds of jobs appeal to you, and which programs may prepare you better. Talk to the admissions officers and look up the career paths of past students. Where did they end up? Is that where you want to be? Keep in mind the kind of life you want to live and the kind of work you want to do. I personally find anything financially or profit driven absolutely soul-sucking, but enjoying doing almost the same work in the medical field. Different skill sets, different programming languages, and different vocabulary are required, and the more you know before you enter the field the better you can prepare yourself for the the journey to come.

Regardless, have fun, and don't worry too much about making mistakes. No one knows how things will work out in the long run. You can prepare yourself with as much knowledge as possible, but you'll never know which was the truly right choice, just which one was your choice.