Everything that Brownymaster, Flame, and mikejs is saying is true, despite the contradictions. Software is a HUGE landscape and every company, market, and subdiscipline of engineering will look at your resume differently.
Flame and I were in the same program at Rutgers and were pretty much roommates. I took a slightly different path since I didn't graduate. We're both "software engineers" now...but I doubt we'd be able to get a job at each others' companies.
As for the CompSci vs CompEng thing:
Flame is adamant about this because the CS program at Rutgers was a joke. I don't know how it is at other state schools but it's probably similar. Keep in mind that switching your major from CompEng to CompSci should be pretty painless...you won't lose anything by trying.
If you go to a top school like Stanford/Waterloo however, you should be set with any technical degree really.