Aldi and Lidl are each other's biggest competitors. Aldi Süd and Nord don't really clash because there is only two markets where both are present: Germany, where they aren't competing though (split in North and South) and the US (Aldi vs. Trader Joe's). Every other country only has one of the two Aldis. Lidl on the other hand is present in most large markets alongside one of the Aldis.