Degree in CS or SE makes a good paper to wipe your bum with unless you have the experience to back it up or were lucky enough to gain a graduate placement.
No one will employ you without some experience so any graduate who graduated and never worked even part time in the industry they want to work in will find it hard to compete with all the other graduates who did part time work even if that was callcentre desktop support.
The name of the degree doesnt matter as all graduates would be lucky to be part of a development team straight after uni. Most end up in shitty jobs like desktop support callcentres to 'build up experience' for 2 years or so they can have the necessary experience to be part of a roper team.
Others end up maintaining code and fixing bugs. After few years they might get on the development team and by then the stuff they learned at uni is only general knowledge considering how quicky technology moves so they would likely be specialist in the stuff their company does but if they lost that job they would be once again behind the tech curve and would need to keep up.
At the end its all about what uni does what and how they approach and name things. The CS ones are ones with stronger ARTS framework and you end up doing alot of general stuff like Philosophy and Logic, alot of Electronics and hardware and heavy Statistics classes coupled with some crazy math you will rarely use as a programmer and if you had to use it likely it was already automated in someone elses library of functions or yo9u just google the formula and copy paste. :)
the SE unis are the ones with more industry contacts that do specific programming courses to get you ready for the job, they will likely have an internship with said 'sponsors' and you wont have to suffer through a 2 year help desk job to build up your experience.
if all else fails CS students should not be discouraged, they can come work with me in the warehouse as a labourer and load/unload containers all day. they 'good' computer skill will come handy with clerical paperwork and they will be a clerk for the rest of their carreer :) shit pay but at least you get undisturbed access to Slashdot :) :)