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.
In my experience, the only time your academic credentials matter very much (if you go to work in industry, which I did) is at the very beginning of your career. At that point, it's more or less all the company has to go on. One or two jobs in, they are only looking at your past experience.
One thing to consider, though, is for those first jobs, it is quite possible that the person doing the interviewing/screening is going to be knowledgable in your academic field, and they will know the difference between a project and a thesis.
Another thing to consider is that a thesis is a real commitment with a bunch of picky requirements and you should be sure you really believe in its value before deciding on that course.
I would, at the very least, talk to some people in industry who hire people with master's degrees like the one you are considering and see if it matters to them (this would help inform the decision that shane describes regarding whether your time might be better spent focusing on finding a good internship.
Tim's comment on your original post is a good thing to consider, and I've heard other people say things along that line as well--completing a thesis is proof that you can actually complete a substantial project. If they are looking at a dozen recent master's' resumes, that could make yours stand out and be a selling point for you.