I kinda agree, I did SE at a Canadian school. (double major with Math)

First year was general engineering: programming, statics / mechanics, chemistry, math etc..

Some courses fill out the engineering side: ex physics courses on: electricity and circuits in 1/2nd year, or waves/optics in 2nd year.

Low level courses like embedded systems were designed to be combined with electrical engineers and would be different in CS.

Some middle level courses are the same: ex data structures, network communication, operating systems

Others that would be CS courses are SE courses: software testing, requirements engineering, dev in teams, large scale design

Some upper level CS electives replaced with upper level SE: Software Reliability and Quality, Process and Project Management, Performance Evaluation.

I feel (and all my friends I graduated with) that the upper level SE courses were all a joke. Large scale design was bad just in our school. Requirements Engg, Reliability, process management, and performance eval were all jokes with nothing useful in the real world (in theory - yes, but in practice you wont use these skills and we didn't learn anything valuable)

Some of the mid level ones were great, dev in teams was a fantastic course and the courses on design patterns (large scale design) are valuable. Software testing was taught poorly and could be learned on your own, but is obviously important in SE.

Additionally we had 2 options outside of engineering courses. I know you get a lot more in CS that could be used towards a minor or another major.

TLDR:

I did SE in a fairly poor program. Take CS, take software engineering mid level courses as options (or a specialization in CS if you want). Do an internship and side projects for a portfolio (just going to throw that in).