Cast iron is heavier than carbon steel. That's because its more dense. As such, CI takes longer to come up to temperature but, once it reaches that temperature, it will maintain that temperature. CI will also retain heat longer once it has been removed from the heat source. CI is great for searing meat and other proteins because of these characteristics. But, as
@Seoul Food said, CI is reactive with acidic ingredients. When CI is properly seasoned, it has very good non-stick properties. Its also very durable. You really have to go out of your way to damage cast iron.
Carbon steel, on the other hand, is lighter and as such, heats faster than CI. The fact that its lighter also makes it easier to handle. It also heats up quite evenly as compared to stainless steel. It can also withstand high temperatures that would otherwise damage other cookware. Like CI, CS should be properly seasoned. Once seasoned, CS is rather easy to clean. Just use hot water and a light bristle brush. Soap is generally not required but, when it is, use a gentle soap to avoid harming the pan's seasoning. On that score, you don't have to worry about any non-stick coating flaking off into your food. Properly seasoned, the pan is inherently non-stick and with a little up keep every now and then, will retain that non stick characteristic for a very long time.
The downsides of CS is that is not dishwasher safe. It must be hand washed. Because of its iron content, its also reactive to acidic ingredients. Also, because of its light weight, it may not be the ideal choice for dishes that require a heavy gauge pan or skillet. It will definitely get the job done. But, as the others have said, if I'm going to pan sear a steak, I'm going with cast iron.
To sum it all up, CS is essentially a lighter weight version of CI that's easier to handle, easy to clean, can handle high temp cooking and is far more durable than almost all other cookware.
I hope this helps.
Good luck!
