Columbia GS students take the same courses as Columbia College (CC)-- although they would be assigned to different sections for the core. You can see an example here for the Lit/Hum course – http://www.columbia.edu/cu/bulletin/uwb/subj/HUMA/_Fall2017.html – Humanities CC 1001 is for CC students only - and then if you scroll down the page, you’ll see Humanities GS 1001 – same course, but different sections. But for almost all other courses outside the core, enrollment is open to all schools and there will be a mix of students in classes.
My daughter is a Barnard grad and when she was in school she felt that the smartest students in her classes were the GS students. So nothing wrong with being in the company of those students – and probably a benefit in the core classes. (I think my daughter’s perception of “smarter” was just a function of greater maturity & life experience – she said the GS students caught onto concepts more quickly)
But it’s not clear to me whether List students are required to also take the full Columbia core. If so, that could limit their options as to courses taken, given that they also have to complete all required courses for the List program.
Also, if you would qualify for need based aid, there might be a difference depending on program. See http://www.jtsa.edu/list-college-financial-aid Barnard meets full need of all students, and List/Barnard financial aid is shared – so I assume 100% need. But that could be dependent on number of credit hours at Barnard - see https://barnard.edu/dos/academic-advising/jts
For List/Columbia students, the financial aid comes from List alone, and it is not clear to me whether they promise 100% need. - their web site says " List College meets up to 100 percent of demonstrated need for all students who are eligible". (“up to” isn’t the same as “always”)
I don’t know the ins and outs of the dual programs, but I think that your daughter might find Barnard to be the more supportive environment overall. Barnard students have strong relationships with their faculty and administration. Columbia, not so much.