However, make sure that the core goes up the sides of the pans for even heat all around.
They make some budget-line pots (such as Emerilware, I think) where the copper core is only on the bottom of the pan, not up the sides. Don't get me wrong--they're still great pots. But they're not as good as regular up-the-sides All-Clad. You'd rather have the regular stainless/aluminum ones than ones that only have a core on the bottom, even if that core is copper.