three mass drive train model is more accurate and gives more high transient but it requires more time in simulation. the two mass model is derived from three mass model, which is also significant in wind turbine grid connected during fault condition. One mass model is very simple can be used in simulation, which includes complex grid with many nodes and thus the wind farm can be considered as PQ or PV nodes in power flow calculations.

See this paper, i added in simulation grid fault with two mass model:

https://www.researchgate.net/publication/269762195_Modeling_and_Optimum_Power_Control_based_DFIG_Wind_Energy_Conversion_System

Article Modeling and Optimum Power Control based DFIG Wind Energy Co...

Two-mass model is the simplest model to take into account the eigenfrequency of the drive train. Higher order models give insights on the influence of higher eigenfrequencies, which are important aspects in, as Kamel has shared, analysing transient loads. However, knowledge of higher eigenfrequencies also give insights on steady-state loads in the form of sustained resonance vibration. In this two publications, I discuss the benefits  increasing the order of the drive train model from two-mass to five-mass and even higher.

http://www.nrel.gov/docs/fy14osti/58960.pdf

http://www.nrel.gov/docs/fy14osti/59195.pdf

The excitation frequencies from electric generator are often of high frequency, which can excite higher eigenfrequencies of the drive train. Such possibility is impossible to analyse using two-mass model.

A drive train is there to help transfer the torque from the turbine blades to the generator. The different drive train s have various advantages as mentioned by James and Irving above. The simplest way to view it is to take it as a connector.