Argh. Maybe we should get some real numbers in here. The following figures come from my old Heat Transfer textbook, but should be easily verifiable elsewhere, and may even be available online:
[symbol]r[/symbol] c[sub]p[/sub] k@20°C k@100°C
Silver 10524 0.234 419 415
Copper 8954 0.383 386 379
Aluminum 2707 0.896 204 206
Iron 7897 0.452 73 67
18/8 SS 7817 0.460 16 17
[symbol]r[/symbol] = Density. Unit in kg/m[sup]3[/sup]
c[sub]p[/sub] = Specific Heat. Unit in kJ/kg·°C
k = Coeff. of Thermal Conductivity. Unit in W/m·°C
From this, we see that copper actually beats aluminum by a margin of 85-90% in thermal conductivity. Silver is better yet, but just barely – and who can afford it? Back to copper, being a better conductor than aluminum should mean that thinner cores may be used and still provide even heating, though it is unclear to me what the minimum thickness is, and whether a thin copper core is just as good as an aluminum core of approximately twice the thickness. But copper-cored pans are still expensive in any case, so that’s a consideration. Another thing to remember is that if a pan only has a copper external coating, then that coating is no more than cosmetic and is too thin to affect the pan’s cooking properties.
Speaking of copper exteriors, don’t get the idea copper is the best material just because of its superior conductivity, and that if you have the bucks, you should only buy all-copper pans. There are some foods that demand its responsiveness (say, a delicate sauce that would be overcooked otherwise), but that’s not true of all foods. Match the material to the food; there is no universal best.
You mentioned aluminum’s higher specific heat when compared to iron, but that’s not the full story. What we should be interested in is heat capacity, which is roughly c[sub]p[/sub]·[symbol]r[/symbol]. Aluminum’s low density results in it having a lower heat capacity than cast iron. So? Cast iron’s low conductivity and high heat capacity means that it has a slow heating/cooling ramp but is excellent at maintaining a steady temperature, which is ideal for pan-frying. Aluminum-based pans will reach higher temperatures quicker, and are thus better suited for searing and sautéeing.