The most violent conflicts of 20th century were within Western civilization. Even the less violent but long-lasting cold war was within 'Western' civilization, because though USSR was geographically east, culturally they are not very eastern. Their historical capital/center of culture was St. Petersburg. There are many St. Petersburgs in the West. So, large scale civilizational conflict is still, mostly vaporware.I disagree.
United Europe is not in conflict with the USA because they are all part of the western civilization. When it comes to "other" great powers, they are actually others for the westerners. There is a civilizational difference outside of the great power co-operation/confrontation. The great powers of one civilization co-operates with a great power of another civilization if there is an interest but when it comes "us vs them" the civilizational difference comes to fore. They are known as west and we are known as east for a reason.