Both Columbia and Cornell are extremely competitive. I can only apply to a few more schools, and I am trying to be prudent with them.They are both highly selective. Cornell has slightly higher stats but Columbia has a lower overall and post-interview acceptance rate.
They both attract the same type of students - highly motivated, intelligent, passionate students that bring something else to the table other than academics.
Columbia is more lecture based while Cornell is more PBL.
Both have outstanding international opportunities. If you go to either school and want to do work abroad, nothing will stop you.
That being said, there's absolutely no reason to just apply to one. What is stopping you from applying to both?