For Chilli Crab, my hands down favorite is at Hua Yu Wee, on Upper East Coast Road. Always large nice Sri Lankan crabs, and a thick spicy gravy.
For Black Pepper Crab, it used to be Lucky View at the East Coast Seafood Centre. Alas, the location is now an outpost of the Long Beach Seafood Restaurant.
A recent good example of Black Pepper Crab I've gotten though is at the Pasir Panjang hawker centre somewhat out of town, west, past the Tanjong Pagar district.