It doesn't really matter, except that if they got a Software Engineering degree from a university that offers both, they're probably a soulless cretin. (The actual manner in which their education is judged is based on the quality of the university, and, if you even have the information, the sort of courses that they took.) When I see somebody that willfully decided to take boring software engineering courses, I tend to have prejudicial thoughts about them.
> It doesn't really matter, except that if they got a Software Engineering degree from a university that offers both, they're probably a soulless cretin.
Or you know they could have done a EE degree and decided after they had done enough courses that EE was not their thing and they would probably do Software Engineering so as to graduate with some degree that made use of the requirements that they had already completed and was at least related to what they wanted to do in real life.
That's really hard to give a decent answer to. The answer really depends on the people involved in filtering the applications.
Can you mirror what the job advert lists it's looking for?
A bit more outlandishly, could you identify a person working in or near the position you're after, then google their CV to see what they listed?
For me personally (not that it should be used to base your decision at all) i've never distinguished between either.
Just for contrast someone i used to work with (an electronic and software engineering graduate) detested the idea of anyone without an engineer's charter (himself included until recently) referring to themselves or their education with the word "engineer". More than once he gave graduates a dressing down for using the E word... life's too short for that IMO.