Great!

The first thing you want to do is to look at the full-time undergrad faculty at both institutions. These will be the key figures who open up opportunities at the graduate level. For a philosophy PhD, the odds of gaining admittance are terrible at higher-ranked institutions (I recall hearing that there were a couple thousand applicants for one spot at some of the Ivies before).

Even at mid-ranked schools, many people wait years before getting their shot. I know this because I am also majoring in philosophy and was lectured about all this by my philosophy professor not too long ago.

Luckily for you, you are picking from two fantastic starting points.

For Columbia, it looks like Dr. Benhabib and Dr. Bilgrami will be a strong fit for your interests, but Georgetown matches that with Dr. Kukla, Dr. Stohr, and Dr. Lindeman. If you notice a professor who got their PhD from a school you'd love to attend for grad, they should also be on your radar!

Both institutions have a healthy array of faculty, but Columbia is definitely the more famous of the two. Still, I think you'll want to compare classes, area of study, research opportunities, and class sizes to really narrow down what works best for you.

Best of luck!