Totally biased answer on my part, as I teach students pursuing computer science degrees, but...

The essence of computer science is learning ideas that have a long shelf life, and incidentally learning how to program. As such, a CS degree will typically include classes on algorithms, AI / machine learning, operating systems, networking, compilers, security, distributed systems, etc. Our own CS majors do learn to program in several different languages, but none of them really matter. It's not learning Java that matters in my own class, it's learning when to use O-O techniques and when to use functional techniques and how to test that your program is bug free. (My own class is maybe 50/50 "computer science" vs. "software engineering".)

Conversely, a software engineering degree will spend a lot more time on software, in general, and the processes and tools for managing a herd of developers. If you're lucky, you'll get a class on historical software successes and failures. Learn why bad software engineering killed people with the Therac-25 radiation machine.

What's better for you? Since your ultimate goals are outside of the field of computer science, as such, it sounds like your goals are to "satisfy the prerequisite" and call it a day. However, if you're waffling between CS and software engineering, you might hedge your bets. Depending on the school, the same introductory sequence might work for both majors. Or there may be a path from CS to software engineering without an equivalent path in the other direction. Maybe you only really need to plan out your first semester and leave the rest for later on.