Congratulations on being one of the very few people who have learnt of the existence of Computer Engineering. (I'm also particularly interested in this specific subject field.)
Either way you're most likely going to go into software engineering (albeit with additional flexibility if you enrol in CSE in fields such as firmware/embedded development, digital circuits, etc), so job opportunities if you're just interested in software engineering will not differ much from what I understand.
The question is what do you want to study?
Royal Holloway's CS is more concerned with software development and the theory of computer science as a whole, you're not really going to be touching hardware. The first year looks into some mathematics as well. The third year is basically just optional modules so you're able to pick between cyber security, machine learning and AI modules alongside some other more-different theoretical concepts such as compilers.
CSE, however, is an engineering discipline and thus the first year is exactly the same as Royal Holloway's Electrical Engineering course. You can switch between these in the first year. The second and third years start introducing software concepts, however at least with Royal Holloway, this is more-or-less just the basic concepts of Computer Science that allow you to follow up on any additional self-study of your own. You can still just as easily learn the rest in your spare time anyway, but this requires dedication towards software development. There is still machine learning and deep learning between the two courses, so if you're interested in AI in particular, you can still learn that in CSE. Otherwise, the rest of the modules are loaned from Electrical Engineering. It's not going to be as dedicated as Royal Holloway's EE, but the whole point is that Computer Engineering is supposed to be a hybrid subject.
I will note that you're going to have to conduct a lot of your own research on this, and I strongly recommend attending open days in order to follow up with actual CSE students. The first sentence is a half-joke, but I honestly think a lot of people only do CSE to begin with because they didn't get the grades for CS.