Whisk mayonnaise, Dijon mustard, whole grain mustard, and Old Bay seasoning in small bowl.
DO AHEAD: Sauce can be made 2 days ahead. Cover and chill.
Whisk vinegar and mustard in a medium bowl. Add cabbage and chile and toss to combine; season with salt and pepper.
CRAB AND ASSEMBLY
Pour oil into a large skillet, preferably cast iron, to a depth of 1/2″ and heat over medium-high heat until oil bubbles immediately when a pinch of flour is added.
Meanwhile, whisk flour, cayenne, and 1 tsp. Old Bay seasoning in a shallow bowl; season with salt and pepper. Place eggs into another shallow bowl. Whisk panko and remaining 1 tsp. Old Bay seasoning in a third shallow bowl; season with salt and pepper.
Dredge crabs in flour mixture, shaking off excess, then dip in egg, letting excess drip back into bowl. Coat in panko mixture.
Working in 2 batches, place crabs, shell side down, in skillet and cook until golden brown, about 4 minutes per side. Transfer to paper towels to drain. Season with salt.
Build sandwiches with buns, sauce, crabs, and slaw.