I don't know much about Harvard but I worked at Scripps and went to the Open day. Here in Europe, it's considered by many the place to be for synthetic organic chemistry, mainly because of Phil Baran's lab really taking off in recent years. But there are other great labs, KC and Jin-Quan Yu to name a couple. Harvard obviously doesn't need an introduction in that respect.
I personally chose to work at an institute because I felt the bureaucracy of a big university can sometimes be a hindrance and in a way that's one of the reasons why these institutes are built in the first place. If you're desperate to TA, you can TA the graduate classes as a senior PhD student.
Again, I don't know much about Harvard so all I can say is Scripps is a great place to go and can really make your career take off. However, if you end up at either of those, you should have a great, though quite intense, research training experience. All in all, there is no 'bad choice' at this point.