Is Princeton better than Harvard?
I think a lot of it depends on what you personally are looking for. Don't choose a school based off rankings. I got into both and chose to go to Harvard as I felt both the academic and extra-curricular government opportunities were better. Princeton is known for its engineering program. Also note the social scene: eating clubs at Princeton versus finals clubs at Harvard (they are very different) and look at Princeton's grade deflation policy. At the end of the day it is all about what's the best fit especially when choosing between two very excellent schools.
Both are very prestigious colleges. Princeton and Harvard usually take the #1 and #2 spots in rankings, but the order switches depending on the formula used.