If you're looking for a high paying software dev position, then Software Engineering is going to be the move, typically with a Computer Science degree. Computer Engineering is more commonly known has Hardware Engineering, so the difference is that with Hardware, you're actually working on the physical hardware, like phones, computers, etc. whereas Software, you're working on the Software that runs on those tools, so you could be working on Apps, Security, Operating Systems, etc. etc. They both pay competitively and there's definitely a need for Hardware Engineers, but software tends to be more popular and pays a little bit more.