Ingredients list from the Coca-Cola UK website:
Diet Coke: Carbonated water, colour (caramel E150d), sweeteners (aspartame, acesulfame-K), flavourings (including caffeine), phosphoric acid, citric acid. Contains a source of phenylalanine.
Coke Zero: Carbonated water, colour (caramel E150d), phosphoric acid, sweeteners (aspartame, acesulfame-K), flavourings (including caffeine), acidity regulator (E331). Contains a source of phenylalanine.
The ingredients list is nearly identical between the two. They both have aspartame. If you don't like aspartame you shouldn't drink either one.