Double offset and concentric butterfly valves are usually soft seated containing some thermoplastic or elastomer seat. This results in temperature limitations and chemical compatibility concerns. However soft seated valves provide better seal performance. The triple offset valve design allows one to get tight shut off without the temperature/chemical limitations.
If we are talking triple offset in lue of gate valves, this could be done for several reasons: space or weight limitations, quicker actuation time, throttling application etc.