<p>In my experience, for those going into academia, it is very helpful to absorb different approaches and points of view. This would be especially true in schools that have relatively small (albeit high quality in the case of Princeton) departments. I think I broadened my perspective substantially by attending three schools.</p>
<p>There is no big advantage at cocktail parties per se, but it is helpful when job-seeking or job-switching if you are known and respected by people at different schools.</p>