Distribution Static Compensator is an important device in correcting power factor, maintaining constant distribution voltage, and mitigating harmonics in a distribution network. This paper focuses on the comparative study of the control techniques for voltage source converter based Distribution Static Compensator, broadly classified as voltage controlled and current controlled. Under the former, phase shift control is compared with the latter, considering indirect decoupled current control and regulation of AC bus and Dc link voltage with hysteresis current control. The first two schemes have been successfully implemented for Static Compensator control at the transmission level for reactive power compensation and voltage support, and are recently being incorporated to control a Distribution Static Compensator employed at the distribution end. The following indices are considered for comparison - measurement and signal conditioning requirement, performance with varying linear/nonlinear load, total harmonic distortion, DC link voltage variation and switching frequency. The paper briefly describes the salient features of each strategy, with their merits and demerits. A dynamic simulation model of the Distribution Static Compensator has been developed for various control strategies, in Matlab/SimPower System environment.