i think of them like this in terms of both prestige and admissions difficulty:
- Princeton = Yale
- Dartmouth = Williams
Some will say that the best education for you, as an undergrad, will be at Williams, since it is a premier Liberal Arts College - and, as such, features a 100% undergrad-focused atmosphere with very small class sizes, ease of access to professors, etc.
And it is true that your average class size, over four years, will be smallest at Williams. Because of that, you will have great access to professors.
But…
Yale and Princeton are two of the three best, and most prestigious, universities in the USA and (for that matter) the world. As a Tiger or an Ely you get Nobel Prize winners, writers of textbooks, and otherwise top minds in their fields as your teachers. There are more students so your classes will be a bit larger for your first two years, typically, but once you are into your major-specific classes you’ll experience smaller class sizes. They do more meaningful research than is conducted at LACs (even top-notch LACs like Williams), so if you are into the cutting-edge stuff, Princeton and Yale are better than Williams.
Dartmouth is an outstanding school with teaching that equals, or seriously approaches, the quality found at the other three. Its national and international reputation is bigger than Williams’ but smaller than that of P and Y.
Princeton has its eating clubs, Yale has its residential colleges, Dartmouth has its Greek party scene, and at Williams the jocks mix with the nerds. Students at all four tout the social aspects of their schools. Probably you could enjoy ypur time at any of them, but “fit” is important, so you should do additional research into their social vibes.
All four are very selective. P and Y are a bit more selective than D and W.
Each school has its charms. Probably the easiest thing would be to get into only one of them, thus saving you a hard decision. But if you are lucky enough to have to choose, your selection will not (cannot…) be wrong.
Good luck!