When I made decisions about what schools to apply to, I talked to several current students and graduates of multiple programs. Whenever I brought up concerns about the job market, they all pretty much laughed and said if you have a stats PhD you will be just fine. I wouldn't worry too much about market saturation.
If you are absolutely convinced you want to do industry, I would recommend working for a while. You should also be just fine getting a job with a masters and you will get an opportunity to see if you are satisfied with the career opportunities you will have with a masters. I think the biggest difference is if are you interested in research or applied work. Jobs you get with a masters will likely be less theoretical and more in the line of data mining than statistics. Also, I would imagine if you eventually want a leadership role, a PhD would be a good idea.