The only difference lies in how difficult it is to get started.
"After Hannya, Inugami, and Huajing, they might not be able to directly receive a Shrine authority that suits them as well as the little Baku did. If they choose an authority that isn't a good fit from the start, they'd have to learn from successful experiences like Mary's operation of faith and find some ways to acquire the corresponding faith."
That's how Kamiyagawa summarized it.
However, so far, he has only been able to raise his Shikigami to Rank B.
If he really wanted to become the co-lord of spirits and demons someday, he'd have to be bolder and aim to raise Mary and the others to Rank A and Rank S as well.
The choice of Shrine authority the Shikigami make at Rank B could directly impact their promotions to Rank A or S later on. Kamiya vaguely guessed that these choices might lock in the Shikigami's potential paths and means to evolve towards higher levels in the future.
...
In reality, at night,