Agia Napa probably slightly larger than Protaras. But since there is a lot of new properties being built in both places it is difficult to say
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Ayia Napa has got the largest themed waterpark in Europe - Waterworld, which everyone should visit. There is also luna park in the center of Agia Napa, near Mc Donalds.
In Protaras there are two places that I would recommend to see: Ocean Aquarium (with lots of different types of fish and also crocodiles, little penguins etc.) and Magic Dancing Waters, spectacular show with dancing fountains.