I don't have enough karma to make a real poll so I guess just say yes or no in the comments.
No.
My impression is that most "Computer Engineering" programs--I suspect that "Software Engineering" is similar as well--are less flexible. With the EECS major you're free to basically do anything related to computers; "Computer Engineering" on the other hand is more about lower-level CS and some high-level EE. You could specialize in Human-Computer Interaction, AI or Machine Learning in EECS, which are all fields that (as far as I know) do not fall under "Computer Engineering".
However, my only real experience is with my university. I only have a vague idea of how exactly this all works at other universities, but they seem to split the subject area I'm covering into two or three different majors. If EECS is what you meant by "Software Engineering"--it is computer related, and it is in the college of Engineering--then I am taking it, and don't regret my choice at all.
I talk to a lot of people currently in school and who have graduated from CS who complain that CS didn't prepare them for the real world and there are a lot of concepts they will never use from a CS degree anyway.
My thinking was that CS is to SE as Physics is to EE or something along those lines. That is, CS as its currently taught isn't theoretical enough in my opinion. I could see a pure CS degree dropping such courses as databases and operating systems in favor of more algorithms and statistics or more programming language classes.
I think CS can make a person a very strong programmer but I can see how many people just don't care for the more theoretical aspects.
I'm currently taking computer engineering and I really enjoy it. It is a mix of CSC and EE and unlike our CSC or SE majors, it requires taking higher level math and physics courses which are needed to analyze complicated circuits. I've grown to like developing software more, but it is valuable and interesting to learn about hardware as well.
Take whichever sounds more interesting to you, but in the long run, there isn't much of a difference. Also, you should be able to take some technical electives to learn specific skills.