Funny, the exact same question came up today. I'm curious what the actual difference between the two is as it's not apparent. (I use a mixture of function prototype with the extends pattern and CoffeScript which exports a function exporting a function.) From what I can see they behave the same as long as you follow the same pattern when writing a subclass.
The main difference in many cases is memory usage. When cloning in prototypal inheritance, you point back to the prototype's function, unlike classical inheritance where you are copying methods on every instantiation.
Prototypal inheritance is native to JavaScript while, simply because JS doesn't have classes, you have to go through quite a lot of troubles to make classical inheritance work.
