The way They look to me, the multi-clad is tri-ply SS with an aluminum core throughout the body of the pan. The Classic is different in that it has a tri-ply disk on the bottom of the pans and the rest of the body is a single ply of SS.
If you can afford the multi-clad go for that. It is heavier duty and will provide for better/more even heat distribution throughout.
"If you want to make an apple pie from scratch, you must first create the universe." -Carl Sagan