Columbia is certainly the better option in terms of reputation, academic and otherwise, resources, and location.
The core/p.e. requirements at Columbia are quite distinct for the school of engineering, but the breadth of offerings there is so fantastic, and really must be a huge draw.
Beyond that, I was in Morningside heights last week and if I take it from your approach to this topic that you're sufficiently academically curious and ambitious that that element will take care of itself, other factors can play into the decision. The students seemd phenomenally friendly, bright and genuinely happy to be there, which was very important to me when I was choosing a university in the States.
It's worth elaborating on the "isolated" nature of the campus, too. Its a healthy balance, as the campus has enough of it's own section of New York to be accessible, manageable and welcoming, but is at the same time part and parcel of the City's life, which I think is brilliant. It can be everything or nothing to the student.
All in all, I was impressed and I would go to Columbia in a heartbeat.