It varies from campaign to campaign. Sometimes a stack of great clans survive to make life difficult, other times it is the "minor" clans which take hold. The most constant message I get is the destruction of the Oda, it doesn't always happen but it happens pretty consistently at times.
The AI can vary its approach to each clan in a new campaign, even when you are playing the same clan as before. Prime example would be the Uesugi. Sometimes they head eastwards, and often clash in a losing war with the Takeda, and other times they head westwards to secure their borders, taking out the few clans up that way like the Date.