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From what I'm aware, diet sodas have a higher amount of water in them then regular sodas do, making it a thinner substance, which give them a lower freezing point. And as Colleen has mentioned, artificial sweeteners are substituted for regular sugar in diet sodas, and artificial sweeteners are lighter in weight.
Sugar in the regular Coke makes it slightly denser than the Diet Coke, so Coke takes a little longer to freeze.
probably the different ingredients within the two