Yale undergrad and NYU undergrad are quite different. In the old tradition of liberal arts colleges, Yale offers no "pre-professional" undergraduate degrees in any subject--therefore, no BFAs. You can get a BA in Theater Studies, but that is more like majoring in Dramatic Literature, even though there are acting classes. The active undergraduate theater community at Yale is fueled and organized by students. NYU undergrad on the other hand offers BFAs which involve more conservatory-style training at one of the various studios that make up the NYU BFA.
As mentioned previously, Yale undergrad and the Yale School of Drama are separate entities. NYU undergrad BFA and the NYU MFA in acting are also separate entities.
Juilliard accepts 18 acting students each year--about half BFA and half MFA.