Big: Except descrbing something huge than average size, it also means large in degree, or something important / major. For instance: "You two are in big trouble." "You took a big chance."
Large: Different from big, large is mostly descrbing soemthing bigger than usual in number and amount. When we emphasize the "quantity" of things, we would use the word "large." For instance: "Young kids carry the large amount of crack."