No. Princeton has a much better undergraduate program. Harvard's strength lies in its graduate programs: Law, Medicine, etc.
Answer -- One is not better than the other; both schools are among the top colleges in the U.S. as well as the entire world, really. Princeton is much more undergraduate-oriented (it has about 5,000 undergrads and about 2,500 grad students), while Harvard tends to focus more on its graduate programs (Harvard has about 6,500 undergrads and about 12,000 graduate students). Nonetheless, Harvard's undergraduate programs are still top-notch. For those accepted to both Princeton and Harvard, Harvard tends to win the cross-admit "battle" (i.e. 65% who accepted to both go to Harvard, and the other 35% go to Princeton). That may be more because Harvard has the most international prestige (although prestige alone is never a good reason to apply to a college). All-in-all, you can't go wrong with either college. Many people in the end tend to prefer Princeton for their undergraduate studies because it is in more of a college town (unlike Cambridge/Boston), and students tend to be less stressed out (it's still very competitive, but students are, overall, happier). It just depends on who you are and what your preferences are. In the end, you really can't go wrong with either school. I happened to get accepted to Princeton and rejected from Harvard, so obviously I'm going to Princeton. If I had been accepted to both, it would have been a hard choice to make, and I don't know which one I would have chosen. But again, each institution is extraordinary, and you'll be able to make the best for yourself at either school. Here's a (sort of) rule of thumb I've heard from a lot of people: Princeton undergrad and Harvard grad is the best combination. Whether this is true or not, again, lies with you and your own preferences. But I've heard this college plan described as the "Nirvana" of one's college career. Just a thought.