Hi, 3rd year EEE student at Strathclyde here
The first year course for EEE and EME are the same except for two classes.
While EEE do programming, EME do "heat & flow" and while EEE do physics, EME do mechanics.
Several people in my year switched between EME and EEE during first year, so if you pick one and change your mind you should be able to swap provided you're not failing all your classes.
In the later years the degrees become more different.
The EEE degree is pretty much split 50/50 electronic and electrical for the first two years, and then in 3rd year you start to make choices and can choose which side of things to focus on.
The EME degree is less electronic, with much less emphasis on programming, and more on power and energy generation.
The employability for both courses is equal, and the opportunities for scholarships, summer placements and graduate jobs are open to everyone.
At Strathclyde there are a lot of links to power and energy companies so if that's what you want to go into, provided you're hard working you shouldn't have much of a problem getting placements/jobs.
If you're interested in other areas there are also lots of opportunities, and loads of people to help you with applications/references.
If you have any more questions I'm happy to answer them