I can’t offer you a great answer because I only just got admitted to Vanderbilt; however, the professors and students all seem very kind. In fact, I have already had multiple opportunities to connect with both professors and students, and I have to say that the small student body is already showing to be a positive.
In regards to prestige and name brand, I believe Duke and Cornell are more prestigious than Vanderbilt and Duke is more prestigious than Cornell (at least in the US… I believe Cornell may have a bigger name internationally). If I was you, I would do more research on the type of environment you want. If you want a small and prestigious school, Duke would be my recommendation. Cornell does, however, have numerous benefits that small schools don’t offer (more clubs, possibly more research opportunities available, etc.) that you may want to consider. I would still go Duke though if I had a choice. Also, you may want to consider where you have the best chance of getting into. Vanderbilt is less selective than Cornell and Duke. Good luck.
Edit: If you are doing CS or Business then Cornell is better than both Duke and Vanderbilt. Still go for fit though. All three schools are fantastic.