Frankly I think Yuji's deleted answer hits the nail on the head, in that concerning yourself with the sociology of various departments is rather a bad idea. "Mathematician"'s answer is essentially the opposite of this advice, making very generic claims about the nature of researchers in various departments, and I believe this is poor advice.
The exact purview of various university departments are not constant across different universities. I know physicists working in at least 5 different departments (physics, mathematics, materials, chemistry, engineering), and mathematicians working in a similar number (mathematics, physics, computer science, biology, engineering). Even talking in generalities, theoretical physics can be found in either its own department, or as part of physics or mathematics departments depending on the university. Making claims about what research papers will look like based on the departmental affiliation of the author is crazy. I myself wrote Theorem...Proof type papers while in a Materials department, and wrote papers without such structure while in a maths department.
When choosing where to do a PhD, you should choose it almost entirely based on the supervisor, not other factors. You'll be shaped far more by your supervisor and their group than by any other factor in grad school. Forget about what department they are in. Many universities don't even include the department on your degree. When asked what their PhD is in, pretty much everyone gives the area not the department. The factors which should really concern you are things like whether a potential supervisor wants to work with you and whether you think they would be good to work with, whether their research is the kind of thing you are interested in, whether they give their students much of their time or whether they are absentee supervisors, the funding situation, etc. None of this is department specific.
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