I concur with all the good insight posted above.
A real-life experience....D applied to several schools as an undergraduate...and the only 2 she didn't get into were Duke and Columbia.
Fast forward four years. She's still the same type of candidate...great grades, interesting EC's, and excellent LORs. This time, she WAS accepted to grad school at both Duke and Columbia. She picked Northwestern

(I think she rather enjoyed turning THEM down this time.)
I'm sure it depends on the program you're applying to, but her experience is that it's easier to get into the uber-selective as a grad student.