IATA.

ICAO is for the actual flying stuff (safety, etc...): it is a public inter-governmental organisation and is concerned primarily with regulatory and safety matters.

IATA is a private body (essentially an association of most commercial airlines other than LCCs) and deals with the commercial stuff.

For instance, if you are a pilot, you will be using ICAO airport codes for your flightplans, etc... Your flight from Heathrow to New York JFK will be from EGLL to KJFK. If you are a ticketing agent, you will be using IATA codes, and the flight will be from LHR to JFK.