Easy answer: Fortunately, NOT an either/or choice. Both traditional undergraduate colleges of Columbia University (Barnard College and Columbia College), have completely separate admissions departments and distinct critieria for their classes - you would want to apply to both to “double” your odds for Columbia University.
If CU is your definite first choice, then, yes, applying ED to whichever of the two university colleges, will substantially improve the chance of admission to that college.
Since you mentioned engineering:
https://barnard.edu/beyond-barnard/4plus1-pathways/4plus1-pathway-engineering