A lot of grad programs in the future are going to look like this; there are serious advantages to experiencing the research cultures of different institutions. As a multi-institutional program, there is exposure to a high diversity of research areas that span the entire set of cutting edge computational approaches being used in many disciplines. For example Sloan Kettering has a very strong cancer focus while Cornell has additional strengths in medical genomics and other areas of computational biology.
Since a student here (as in any program) is going to be doing focused work on a research question, the most critical thing is to find an area that interests you, that you can really get your hooks into intellectually, that will drive you from a research perspective,. However, there is also the chance to be immersed in the cultures of multiple institutions while you are in graduate school; being exposed to different perspectives provides very useful knowledge for how to approach research; this translates into students bringing a diversity of techniques and knowledge into the work of their PhD. program, a student here is going to be attached to a single main advisor and they are going to be doing focused work within their research program. The most critical thing is find an area that interest you, that you can really get your hooks into intellectually, that will drive you from a research perspective.