I am appalled by the amount of misinformation on this topic. I've been teaching engineering for many years in a BSE program and know firsthand the difference between a BSE degree and a BSME or BSEE degree. Here is my analysis:
BSE (Bachelor of Science in Engineering) and BSME/BSEE are both legitimate engineering degrees from ABET accreditation agencies and from employers.
BSE is considered a general engineering degree and emphasizes multi-disciplinary engineering training (in other words, crossbreeding), while BSME/BSEE is considered a more narrowly focused degree on specific fields of engineering. There are pros and cons for both degrees. Some employers prefer to hire BSE's due to their well-rounded educational background in liberal arts and multiple engineering disciplines. Face it, the real world is a highly integrated work environment and rarely would an engineer have the luxury to only work with engineers in the same field. Multi-disciplinary exposure and education is in general more desirable to potential employers than a narrowly focused field of study. Most smaller colleges go the BSE route because of their strong liberal arts education and their focus on teaching. Most large universities go the BSME/BSEE route because they emphasize research. For BSE programs, the first two years the curriculum for all engineering majors are almost exactly the same. You will have opportunities to be taught by professors from multiple fields and you will have opportunity to work with fellow students from many disciplines. This multidisciplinary approach to engineering education is BSE degree program's strength. Graduates from these programs generally have an easier time transitioning to their jobs and have better prospects of becoming engineering managers or project managers.
For a proof of companies treat the two degrees the same, simply go to General Motor's job website and take a look at some of the engineering job descriptions.
https://search-careers.gm.com/us/en/search-results?keywords=engineering
Some postings would say BSE or BSME required. Some would simply say
Minimum Education Required
• Bachelor’s Degree in Engineering
In a nutshell, BSE is not a degree that is inferior to BSME or BSEE. Often times it is superior to a BSME/BSEE due to its broader training and more flexible career outlook. Plus, engineering education in a smaller college setting allows students more opportunities to work with professors and professors are in general better teachers than professors from research-focused universities.