It's state dependent. There a large number of states that don't recognize the SE as a separate license yet. I would use it on a resume sent to a state that does recognize it. For me, I am sticking with the PE title I already have. That's not to say you can't use it in a signature or business card. It's just that some clients or agencies may not know what it is in a PE-only state.
Does someone who passed both exams, in a state that doesn't use the SE title, gets to use a PE title in its place? In other words, do you get your PE license? I never bothered looking into this one because I have mine already. But I imagine there are some people taking this test as their first set of exams.
djsarata,
You are right, it is state dependant.
For me personally, I am a PE in MN as well as an SE in CA, IL, and WA. Granted I could use both titles, I simply choose to stick to the PE title until MN becomes an SE state.
As for your last question, a good example is IL. IL has an SE as well as a PE. If you are able to take the SE exam and pass, then you get the title SE only. If you choose to take the PE exam and pass, then you are a PE. If you pass both, then you have both.