I think that the capacity to dictate terms after winning a war (a la EUIII, but without infamy). Hypothetically, if you're pressing a claim to a province or duchy and manage to occupy and hold significant other territory, you should be able to claim all the territory you hold.
Also, can the implications of capturing a ducal or national capital have greater implications. Occupying Paris or London should matter more than it does. In the case of Byzantium, Constantinople should be both harder to take, and worth more when you do (like in 1204, when the Crusaders taking the city basically caused the entire empire to implode).
Demanding more than you initially went in for could also enhance your prestige, proving what a successful warrior you are
Also, can the implications of capturing a ducal or national capital have greater implications. Occupying Paris or London should matter more than it does. In the case of Byzantium, Constantinople should be both harder to take, and worth more when you do (like in 1204, when the Crusaders taking the city basically caused the entire empire to implode).
Demanding more than you initially went in for could also enhance your prestige, proving what a successful warrior you are