Civil engineering will get you a job.
Electrical engineering is more interesting but less likely to get a job.
I am a final year Electrical Engineering Student with Job Offers from ASX200 Companies, so I think Im in a pretty good position to give you some advice.
Firstly, Electrical Engineering is very mathematics focused in a few areas.
There are less maths heavy electrical engineering areas.
The main areas of electrical engineering are
Control Systems, Communication, Signal Processing, Power System, Electronics. Out of them the communication and signal processing are very maths heavy, power and control are less so and Electronics is mostly about logical thinking.
So it's possible for you to specialise in less mathematics heavy areas, though some of the areas like communication, power and control are in demand in Australia.
Coming from someone who has worked in the industry and have contacts in the private sector, I would really recommend you to go with the area you are more interested in, look at it this way, this is an area where you will most likely be spending 20-30 years of your life down the track, and University is only a small aspect of your future.
I know definitely when you enter the work force, the technical work you do is 10 times easier than what you were taught in University. Most likely you will end up in management roles since engineers are so expensive, so there will be much less mathematics and hardcore engineering when you start working, unless you work for specialized branches of consulting.
Unlike what people said, currently all engineering areas are in a downbeat market, but if you are doing civil, electrical, mechanical and chemical you will have better chances than others.
Currently, if you study engineering, due to the mining downturn, you need to be quite good with good experience and OK marks to land a job anyway.
Academic marking only contribute perhaps 1/3 to 1/2 of weighting in job applications, typically people with 70+ average can land a decent job, and 75+ gets you into the big players like BP, Exxonmobil, BHP Billiton.
It's more important to love what you do, actively engage with university society, industry and have experiences and extracurricular activities under your belt.