I know one at Joo Chiat which serve good chilli crabs. There are always lots of people queuing up. To go there, you can travel along Still Road and then turn to Joo Chiat. It's at the junction. Easy to find. Open in the evening, around 5pm -6pm. You will see many people queueing up.
The other one is at Ang Mo Kio. Some of them had already given the address of the Ang Mo Kio shop, so I needn't say anymore.
Jumbo and Little Red House's standard are inconsistent. Sometimes good, sometimes bad. And prices are steep! I went to Jumbo recently, it was quite disappointing, the sauce was too starchy that it taste weird. Little Red House is not bad, except for the price.
Little Red House and Jumbo are at East Coast. Very easy to find b'coz they are pretty famous.
Hope I help you.
As for ingredient, hmmm.... Chillies lor, so simple! For chilli crabs, of course it is the chilli. In the past, when I was younger, the version of chilli crab were spicer than now. The current version had change a bit, but it is still nice. Now they add tomato sauce to it. As for the chilli paste, there are lots of spices. So it is difficult to pinpoint which single ingredient make it special. Many restaurants use almost the same ingredients, but I guess its the amount of different spices that varies. Maybe the famous and good restaurants had got the balance of which ingredient to add more, and which one to add less when they are preparing their chilli paste. In addition, the crabs and the cooking time also make the difference. Cooking too long alter the quality of the crab meat. The crab meat will shrink and don't taste good, become watery too. Singapore chilli crabs use crab from Sri Lanka, mostly. The mud crabs, greenish black in colour. I think mud crab taste better when cook in chilli, compare to other types of crab. All these reasons make this dish special.