Should I do a thesis, no thesis, or a capstone project in a master's in statistics? I intend to work in industry after finishing my Masters in Statistics and am considering some universities in the United States. How will a Masters in Statistics with thesis, no thesis or with capstone project impact my career prospects? I've read that having written a thesis that is relevant to the employer's business  would be beneficial. But how does that compare to a capstone project? It sounds to me that a capstone project and thesis mean the same thing as both involve research.
Could you give us some more detail about what the capstone project would entail? That seems pertinent to the question at hand. I'd say that you should try to get a perspective from people currently at work in the industry, rather than academics. My two cents worth is that a thesis would look good if it could showcase your written communication abilities and demonstrate an ability to do self-directed work. But consider the time involved and ask if the time spending acquiring/demonstrating these skills might be better used doing something else equally or more applicable to entering industry, such as networking, internships, or the like. The question isn't whether a thesis is good: it is. The question is whether it's the best use of your time, which we aren't going to be able to tell you a priori, I don't think.