Engineering school generally focuses on making you learn how to think. Even at my current job there are people with PhDs and graduate degrees who can't properly use Google search keywords.
If there's one thing engineering school taught me it's how to work with no sleep, how to pass tests without going hard on studying, how to meet deadlines, and how to balance having little to no 'free' time yet still finding time for exercise, friends, etc.
I'm not trying to knock or downtalk CS because it is definitely a reputable degree and the coursework is definitely worthwhile but when I graduated I had very minimal experience coding, told myself I'd never software develop/code for a career and had no drive to learn. Then when I graduated I got a job for the DOD doing logistics engineering and now 2 years later I'm a developer at a telecommunications company making pretty good money as a software dev despite having legitimately minimal experience ever coding.
I didnt even suck any d's or know anyone at this company but I will also say when you're at school focus on networking with people even if they're shitheads if they have connections. Knowing people is generally more rewarded than knowing 'things' and if you can become friends with the right people it'll make your job searching down the road a lot easier. I got my DoD job through a connection and then this company hired me just because I had gov't experience even though I had 0 exp doing software work.
I'm still gonna back the CE over CS though. CE you can go into a lot of different fields (business,engineering,electronics,software) where I feel like CS limits you to software generally. Also the quality of people you meet in engineering is probably also more rewarding in the long run than the CS dept. For example if you're friends with the smartest kid in engineering it'll probably have better outcome networking wise than the smartest kid in CS.
That's just my opinion though, and my experience.
I graduated in '12 in CE.