The competitors for this bout are Mama Bunns at Gallery32 and Tour Les Jours just down the street on 32nd Street.
Tour Les Jours is one of several Korean-French pastry-coffee shop chains (see also Paris Baguette) that sell huge selections of buns, pastries, breads and cakes that mash-up French and Korean influences (see Red Bean Cream Pastry). Their kimchi croquette is a fried donut like pastry with a thin crispy crust around a light savory bun bread. The filling was finely minced nappa kimchi, onion, sweet pepper, and sweet potato noodle and had a thick sauce texture. The experience was very much like eating a jelly filled donut that had a Korean flavor profile. I thought the filling had a very mild kimchi flavor with low heat. The outside of the croquette was greasy, so you will need several napkins. These buns were decent, not great, but are a good gateway to kimchi.
Mama Bunns sells fist sized, more traditional, Chinese style steamed buns with a variety of filling choices. Their kimchi bun is filled with roughly chopped cabbage kimchi, onion, scallion, vermicelli noodle and sesame oil. Because the cabbage kimchi is roughly chopped, the filling had crunch and texture, it also had a full bodied, fermented kimchi flavor with a strong spice kick. The buns are served right out of the steamer and are really hot, so you have to let them cool a little before you bite into them. I think these kimchi buns are excellent, but eating one is dive into the deep end of the kimchi pool.
The winner of this battle was Mama Bunns, by a wide margin.