I'm in the same boat as you (although I have just finished a first degree) and was worrying a lot about this question too. I looked at a lot of articles online and ended up calling quite a few (really big) games companies to ask them. Some preferred CS degrees but most said it's about the programming (C++) skills that you show you have through your portfolio. Some said it doesn't matter if you even have a degree as long as you can demonstrate good skills.
So just choose the course that you think will teach you how to program in C++ the best.
Just looked at the content of both courses and it looks like the computer science course doesn't cover any C++ where as the Games Software dev course covers it in multiple units. Thanks for the help
Also, as someone who has completed your first degree, did you have prior experience with C++ before starting Uni? I currently program in C#, but would It be worth starting to learn C++ before starting uni?
Aye I have spoken to a lot of CS students who said they learned barely any programming, seems like it's all about the specific course that one is looking at.
There's some great advice in this thread though!
In response to your question, my first degree was in Music so somewhat unrelated. I did CS at A-level (pre-university if you're not from the UK) and we studied Python but that was 3 years ago now. I'm definitely going to spend as much time as I can embedding C++ into my brain before September.