Wow, Congratulations, You're so lucky ! It's such a dilemna.
The both schools are the best for me. nevertheless, I'll choose Yale. I heard that the people there are helpful meanwhile in Columbia, there are all competitive. If you really want to go to Columbia, you still can do your grad or your PhD there.
How did you get in ? Do you think that I can get in ? This is my profile : Can I get into NYU/YALE...?
Thank you, and again congratulations !