That makes software engineering an ideal choice for people not going to college at all. But since you're already 4 years in, you might as well finish. So definitely finish.
Outside of credentialism, there's still the other reason, and I think this is the one motivating the advice you're getting from your friends:
> to compete for a higher position in the social hierarchy
You'll be more effective at this if you wait and go to the higher-status university.
From your current position, I'd definitely recommend finishing your degree, and since we've already optimized for status, I think I would wait and go to the university with the more fashionable brand if that option is available to you.
Top companies write a lot about how they've found no correlation between university ranking and job performance, but then they continue spending millions on job fairs and hiring mostly people out of top universities.
Your friends are right that many companies, especially big ones, will treat you very differently depending on which of these two schools you choose. Good luck.