"A solid defense can act as your best offense, but a powerful offense can be your best defense."
Just as yin and yang are opposites that can not exist without each other, defense and offense interact the same way.
Applications to AOE3:
-When looking to win, sometimes it is best to build/ship outposts/warhuts and walls and hold off until you have advanced your economy enough to outnumber your enemy. This is where a defense can beat an offense. The best civilizations for this are the Dutch (build banks and use your outpost shipments until you can advance and build cannons and halbrediers) and the British (build houses and outposts until your population is high and your economy allows you to harbor a massive longbow or musketeer force).
-When facing an opponent of greater ability, give them no leway. Do not fear their almighty rush, just advance as fast as you can and ship loads of soldiers. Rush them ASAP and while your men are fighting, build up your economy to prepare for a second all out rush. This is where a great offense on your part can help counter your enemy when they are booming, giving you enough time to prepare for a second, greater attack. The best civilization for this is the Spanish with their heavily based military shipments and their well-balanced economy.