Sorry, i didn't clarify myself.
I can't speak based of UNSW but i did attend UTS for SE and Usyd for comp sci.
In CS, you don't actually learn about the process of creating an effective solution for your customer. You only learn the how. You don't learn how to work in a team, how to identify problems in design criteria and how to manage time. You learn to write code, and learn about computers and that's it.
In SE, you do a variety of subjects which force you to work in a team and complete a set task. (Some at UTS include ICT analysis and ICT design which i am sure UNSW has similar subject) Ignoring all the learning stuff, as i stated above, there are only certain jobs an CS can do. Cs's generally can't work on critical systems, even some Se's only those who hold Ieng's or Ceng's (which is very important if you want to move up in $$).
Basically, what i am trying to say is that SE is a far more practical degree. If you want to work on large complex systems with a team, become an SE, otherwise if you want to become your average coder, working on mid level systems, do a cs degree.