| Well, the obvious difference is the fact that Wellesley is basically in the suburbs and Barnard is in New York City. They're both great schools, but at Wellesley you're really getting the isolated, all-girl atmosphere most of the time, and at Barnard you're right across the street from Columbia, where, needless to say, males abound. I imagine also that the student body at Wellesley is a bit more together than at Barnard, because they don't have very much to do outside of college life. Barnard has all of New York; like any city school, the students aren't going to be quite as - I don't know, united, maybe, as they are at a school in the suburbs or in a rural area.
In terms of academics, you WILL take classes at Columbia when you are at Barnard. Wellesley is not particularly convenient to any other colleges - at least, not so that you'd take courses there. Yes, you can get to Harvard, MIT, and other colleges from Wellesley, but it's a fair sight more complicated than walking across the street. I live in that area of Massachusetts and it's not really too close. You could definitely go into Boston on the weekends, but I think I'd find it too much of a bother during the week.
There have also definitely been threads about this before; do a search and you'll probably find some more specific answers from people who know more about both Wellesley and Barnard than I do, given that I never looked at Wellesley at all and I haven't quite gotten to Barnard yet. : ) | 
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