I've been to the Mezquita-Catedral in Cordóba. It's a fascinating building and I do agree that it sort of forms a pair with Hagia Sophia, but I'm having a hard time seeing any influences it may have had on Western church architecture.

Other than the gothic altar section built square in the middle of the building it is very much a mosque with a completely different floor plan from the typical cross-shaped churches common in Western Europe since Romanic times. Even the typical round arches were already outdated in the West at that point in time.