They both have their pros and cons.
Hime gets along with her mother, actively participate in politics, and marries the most (or second most) hated Kitsune. Inari argues with her mother all day, prefers farming over politics, and marries the most chill guy (sadly, he has NO interactions with the player).
They both have the same problem actually connecting with people. Hime won't ever show her true feelings, to avoid getting people worried for her. Inari actively shuts herself from the rest, and tries very hard to be self sufficient.
If you want Kinu to fulfill her role as a princess, fully embrace Kitsune traditions, and become a beacon of hope for the community, go Hime.
If you want Kinu to be more grounded in reality, defying her heritage and traditions, while being the most productive member of society, go Inari.
In the end, this is mostly for roleplay