Andover and Exeter are related. Different members of the same family founded each school. Samuel Phillips founded Andover in 1778; his Uncle, John Phillips, founded Exeter in 1781, Hence, Andover is known as Phillips Academy (PA), and Exeter is called Phillips Exeter Academy (PEA).
Andover and Exeter are also connected in the public imagination. In an episode of the Simpsons, a salesman at a fund raiser tries to sell Homer a t-shirt for the local school his children attend. When Homer refuses to buy that t-shirt because he does not want to be associated with that local school, the vendor says that his two best-selling t-shirts are "Phillips Springfield Andover" and "Phillips Springfield Exeter."
As for Andover and Exeter, the important question is not which is the better school. It is which is the better school for you. That's a question of fit, and only you can answer that question for yourself.
Some differences between Andover and Exeter are:
A. Andover divides its dorms into five clusters; at Exeter, students typically remain in the same dorm until they graduate.
B. Andover has a 1-6 grading system; Exeter has a 1-11 grading system.
C. Andover offers need blind financial aid that admits applicants regardless of their financial background; Exeter is need aware. However, Exeter offers generous financial aid.
D. Andover has one central dining hall; Exeter has two dining halls.
E. Andover has fewer Saturday classes than Exeter.
F. Exeter has a dress code; Andover does not.
G. Last year, Andover had a lower admit rate, a higher yield, and (I believe) better college matriculation statistics than Exeter. Nevertheless, Exeter is extremely difficult to get into, very popular, and does exceptionally well in placing students into top colleges.
H. Exeter prides itself on the Harkness Method (student centered discussions), which it typically uses in all classes, including Math and Science; Andover stresses critical thinking as well but does so through a wide range of teaching approaches that generally do not include the Harkness Method in Math or Science.
I. Some people think Exeter has a nicer campus than Andover; others prefer Andover's campus. Both campuses are very nice.
J. Some people say that Andover is better in the humanities than Exeter and that Exeter is better in Math and Science than Andover. I don't buy that theory. Both schools are generally excellent in all fields.
K. Andover is closer to Boston than Exeter.