Prolog evaluating how two lists compare to eachother?

According to your definition of "greater" there is no need to continue the recursion after you find that X>Y. If you reach the end of the recursion (as chac said) you'll know that the two lists are equal.

In your solution you use (>)/2, (>=)/2 and (==)/2. The first two will evaluate their arguments as arithmetic expressions prior to a comparison. And (==)/2 will compare due to term order.

You will have to decide for one of them or another term order. But you cannot mix them.

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