I don’t think it’s possible to come up with a one-to-one equivalency between the Hogwarts houses and the new Ilvermorny ones. Horned Serpent has a snake mascot like Slytherin, but represents the mind and chooses scholars, which sounds more like Ravenclaw. Wampus and Thunderbird both sound quite Gryffindor, although they are very different from each other and could certainly include people from other houses. And Pukwudgie sounds like a subtype of Hufflepuff, but certainly not the same thing. Even if all the descriptions lined up, the vast number of people across the internet reporting all kinds of different house combinations would be enough to show that there are no perfect equivalencies.
Instead, I think the two different house systems measure different aspects of personality.
The Hogwarts houses represent what a person values. Gryffindors value bravery, Ravenclaws value knowledge, and so on. These values do not even necessarily line up with one’s personality. Hermione, for example, is extremely intelligent, but outright tells Harry at the end of Sorcerer’s Stone that friendship and bravery are more important than books and cleverness. However, characters who start out quite different from their Hogwarts house description usually grow to fit it. Neville is timid and awkward in the early books, but by the end, he is leading Dumbledore’s Army in Harry’s absence and stands up to Voldemort himself when Harry seems to be dead.
Ilvermorny houses, on the other hand, don’t have anything to do with the values that the Hogwarts houses represent. In the Pottermore article, J.K. Rowling explains:
It is sometimes said of the Ilvermorny houses that they represent the whole witch or wizard: the mind is represented by Horned Serpent; the body, Wampus; the heart, Pukwudgie and the soul, Thunderbird. Others say that Horned Serpent favours scholars, Wampus, warriors, Pukwudgie, healers and Thunderbird, adventurers.
Therefore, it seems that the Ilvermorny houses represent the ways in which a person makes choices:
- Horned Serpent is for “scholars” who make decisions based on logic and reason (the mind)
- Wampus is for “warriors” who focus on the practical and immediate (the body)
- Pukwudgie is for “healers” who are driven by love and emotions (the heart)
- Thunderbird is for “adventurers” who are guided by their beliefs (the soul)
There may be certain correlations, Hogwarts houses and Ilvermorny houses that go well together and even overlap in some ways. However, in the end, the Hogwarts and Ilvermorny houses measure two separate aspects of personality: one is based on values, whereas the other is focused on decision-making.