Congrats on getting into Yale and Princeton.
1) Teaching versus Getting a Job - First, it is not true that Princeton students have a disadvantage in terms of teaching versus hire. Princeton EAS as well as related students to the dept have been getting decent jobs (from liberal arts colleges to top universities in Asia to decent research universities in the states) despite the economy. There are plenty of opportunities for you to precept in your third, fourth or fifth year as teachers are always looking for grad students to do so. Most, if not all, students in the department precept for at least one term. Some have gone away and taught in the NY area colleges and universities while finishing up their Phds.
2) Big or Small - Princeton does have smaller sized classes for its seminars, so you do get a lot of attention from the prof. The flip side is that there's a lot of preparatory work to be done so as not to be caught off guard given the size of the class, but that's the point of grad school isn't it? That said, Yale appears to have a larger department overall with more classes available for graduate students. It all depends on the particular field you are interested in.
3) Pre-modern versus Modern - The sterotype is that Yale is stronger on Modern/Contemporary and Princeton on Pre-modern, although modern Japanese history appears more solid in Princeton. In actuality, it probably doesn't matter given the wide range of interests in the professors in both universities.
