Numbers mean more than anything else, but when numbers are nearly equal the better tactical player with weaker units can still win by a large margin. For example, in one game my opponent sacrificed his economy to rush with an army supported by priests. However, as defender I had the advantage of better information, so hid scout cavalry in trees opposite the next anticipated combat zone. When the attack came his troops moved up to the front line, which gave my otherwise weak scouts a perfect chance to hit him from behind. They quickly slaughtered his undefended priests and at the same time cut off his escape from my stronger units.
Strategic combat is what makes most of the difference between otherwise balanced players.
Speed is important. Faster units tend to be weaker but can respond to attacks more quickly, encircle the opponent, go deep past enemy lines without getting caught, help teammates, and push attacks before your opponent can get organized. Strength is important. A mass of very strong can take city after city with no damage while the enemy desperately throws troops in an effort to stop you. You can't just throw units at the enemy and hope to accomplish much unless you are already much stronger.