I want to choose either Informatics or Software engineering at UC Irvine, or Business Admin with Information systems or Software engineering at Cal Poly SLO. Which would be a better career in terms of climbing up the promotion ladder?
Career advancement is a function of job opportunities and how well you do on the job not on the major you take and the school you do it at 
Pick a career you think you’re more likely to enjoy and be better at and with hard work you’re definitely do well regardless of school and major. Both those schools are great, with their pros and cons. Good luck.
Software Engineering. This is more of a specialization and its coming from a UC. I too have looked into this major at Irvine and I’ve found it to benefit the student because Irvine is right in the city where big tech companies are.
UC irvine does have informatics with a specialization in software engineering. That could be a good option.