Absolutely no difference cooking with the two brands - I probably have an equal number of pots/pans from both lines. And believe me, I researched, debated with myself, went to the stores lifting, turning ,etc, looking at every nook and cranny. I think the difference in the thickness is negligible. The biggest difference is probably the handles and the tempered glass lids (which i didn't expect to like and have surprisingly enjoyed - you can actually see through them while cooking/baking).
If I'm going to be honest, the reason I have both is my internal kitchen snob lis just a little infactuated with the whole All-Clad thing, and so I've been buying some here and there. But for cooking - no difference! imho