There's a reason why so many couples put expensive pots and pans on their wedding registries: They make a difference in the food. There are at least a few reasons why.
First is responsiveness, and it's pretty much the same thing that makes gas burners preferable to electric. The faster a pan responds to a change in heat, the more precise control the cook has over the food inside it. Heavy-gauge pans of copper and/or aluminum are highly responsive [source: Cooking Inn]. They also allow for more even cooking over the entire surface of the pan, so you don't end up with food being underdone or overdone depending on where it is in the pan.
Beyond heat management, you might want to invest in a couple of pots or pans that suit particular purposes. For cooking acidic foods, like tomato sauce, you'll want a nonreactive pan or else the food can take on a slight metallic taste. And for cooking white sauces and eggs, it's best to avoid all-aluminum, which can turn those foods kind of gray.