Engineering vs Physical Science

So, I'm a student sitting for my AL examination this time and I wanted to know which is better. Doing a government degree for physical science or joining a private uni like SLIIT for mechanical engineering. (My results won't be enough to do engineering in a gov uni)

What are the job opportunities like both in Sri Lanka and abroad. I have a passion for engineering but I'm worried about the quality of a private degree and whether I'd be able to land a job with it. I also would not like to be a burden to my parents financially as well. Is it possible to help with semester fees by balancing uni stuff and doing classes or working part time?

Also what's the difference between a local engineering degree in SLIIT and a foreign based one (Australian transfer program in SLIIT for example) Is it worth the extra cost?

And no, second shy isn't an option due to different reasons :(