Love these. As with Once and it's wackiness, the correct answer is: It depends.
Both could win, but I'd say 7 or 8 out of 10 times, Cora takes this. Cora is not a slouch in spellcasting speed and is quick on her feet (well, I mean cleaver). She has a restraining spell that she can easily stop Ingrid from doing magic for enough time to take Ingrid's heart. Even at best, Ingrid could summon a creature for distraction purposes and that's probably where it becomes more even....aka when Ingrid can actually pull a move off.
I would say Cora. Only because I feel like her magic is a little more
Powerful. But now that I think about it, Ingrid could freeze her, and push it over. But knowing Cora she probably already thought up an idea thought up a way to get out of the Ice. So it could really be up to any one.
It depends on their environments, truly. I'd wager Cora has a huge advantage in having way more magical knowledge than Ingrid; the former learned and embraced magic by herself, whilst Ingrid spent the bulk of her life trying to contain them, then getting trapped in an urn, then living in a land without any magic to study.
Thus, Cora has a lot more variety to work with; meanwhile, I do feel Ingrid is more powerful than Cora when it comes to raw power. Thus, it's really up to how clever Cora can be.
They're both extremely cold and calculating in their ways of planning and thinking, so I don't believe they one-up each other in that way.