While I do know many EE PhDs that are strong mathematically, even those have typically only taken the equivalent of a BS in math, perhaps with one or two graduate level courses. In the department I was in for grad school, the comms/signal processing / controlls PhD students usuall took most or all the undergrad math courses recommended for preparation for math grad school. If you want to be "treated like a mathematician" you most likely need the math PhD - at least in a university. If you are in industry or a "think tank" then it all comes down to what you produce. If you have a track record of publishing innovative mathematics related to your application area, then you will continue to get that kind of work. Chances are you will also have to bring in some of your own funding, and likely do much of your publication "in your own time." That is what I have seen at my company.
jason