You didn't mention what camera you are using, and that can make a difference.
Personally, I like the 24-70 better for portraiture on a crop camera, than on full frame.
The 70-200/2.8 is pretty large for some types of portraiture, but good focal length range on a FF camera. A little long for some things on a cropper. The "big white" lenses also aren't very subtle for candid shots and can be intimidating to amateur models. Actually, the 24-70 is pretty big, too.
I'd want (and have) smaller, more unobtrusive lenses: 28/1.8, 50/1.4, 85/1.8... 135/2, usually on FF, is my largest. On crop I also sometimes use 20/2.8. 35/1.4 would be fine, too, tho I don't have it yet.
Another reason to choose primes over zooms for portraiture is that, at best, zooms only give you f2.8. Primes can be 1 or 2 stops faster... even while in a much smaller package.
For that matter, for street photography I wouldn't want 50/1.2 or 85/1.2 either. They are simply too big and attention grabbing. They also are slower focusing and a bit more difficult to work with, unforgiving and sort of specialized as portrait lenses, a bit less versatile than some of the "less radical" lenses. On the other hand, if I were a wedding photographer, for example, I'd certainly want the two f1.2Ls for the look they can give, unlike any other lens.
Shooting fashion, the 70-200 is a great choice on crop or full frame. 135/2 and, on full frame in particular, 200/2 are a couple more fantastic choices. In general, fashion is frequently shot with longer lenses. Of course, that also often requires more working space, in-studio or outdoors.
If you are just starting out with fashion and studio portraits, I'd say get cheaper lenses, put your money into a killer light kit and learn to use it well. That will go farther than spending tons of money on lenses. One of the most prolific portrait/fashion photographers I know has for years used a Canon EF28-135 as his primary lens in-studio. You can pick up one of those for $250 or less, lightly used. Personally I'd rather have a handful of primes, as mentioned above. I'd usually look for USM (or equivalent) for focus accuracy and speed. But I'm currently trying out a Tamron 60/2.0 Macro/portrait (crop only), and have been pretty happy with the focus speed. I generally don't care for macro lenses for portraiture, but this one has a stop larger aperture than most and it's always nice when a lens can serve multiple purposes (this one might replace three lenses in my camera bag 50/1.4, 85/1.8 and a macro).