@OrchidBloom, depends on which grad school.
PhD programs (the ones worth go to) will be funded, so you wouldn’t have to pay. I wouldn’t advise spending much money on a JD (outside of YHS). That leaves med school/health or b-school. If the goal is med school or some other health profession, going to the full-ride school makes a lot of sense. For b-school, however, work experience would be very important, and Yale may give you a leg up (especially in certain elite MBA feeder industries).
But it also depends on what program/school your full-ride option is. So the decision, to me, is very dependent on goals and majors.