>>96510176
When in combat, Madoka is more Madoka than Kukurihime, although it's more a result of the Idolon intentionally taking a back seat. Some of Kuki-chan's habits shine through however, like some minor speech habits, posture, etc.
Because it's intentional, it also means that if she wants to or needs to, Kuki-chan can shift to a more active role in the incarnation. If that happens, it results in a very noticeable increase in skill, going from more brute-force usage of powers to intricate layered schemes and extremely precise or more advanced applications of their abilities. Needless to say she's a lot more level-headed and confident as a combatant too.
Some things wouldn't really change however. They're both kind-hearted and like standing out. They're both generally going to prioritize the safety of allies over all else. Very similar mindsets. Kuki-chan is just a lot more wise and capable.