I think I'll take this opportunity to highlight the main difference between CS and SE:
A scientist discovers new things (e.g. electromagnetics).
An engineer uses those discoveries and applies them to come up with solutions to real life problems (e.g. using electromagnetics concepts to create antennas).
That is why Computer Science students take more math courses and later apply it to algorithm analysis etc.
In industry on the other hand, you work as a software ENGINEER. You apply CS concepts to real world application. And for that reason, engineering degrees are a lot more valuable than a science degree. Even if it is in another field (say Electrical, Mechanical, Mechatronics [etc] engineering), your degree will be more valuable than a CS degree. The idea is that engineering courses would have helped ingrain application skills in the student. Of course you still need to have sharp software skills, but those are usually self taught anyways. The more you code, the better you get! Plus you should focus on self-study to learn about better software architecture and design techniques.
Extending on that idea, engineering degrees are significantly more valuable than arts degrees for business/investment jobs as well. I've seen Electrical and Mechanical engineers working in investment firms (stocks, forex etc), heading the whole department. Engineering is one of the hardest specializations you can choose in university and it definitely pays off, as long as you're willing to make the effort!