This paper represents the comparative study of Ant Colony Optimization (ACO) and Particle Swarm Optimization (PSO) for Grid scheduling. The objective of ACO and PSO is to dynamically generate an optimal schedule so as to complete the tasks in minimum period of time as well as utilizing the resources in an efficient way. Makespan is the performance measure used for the comparison of the scheduling techniques. This paper compares both the above said optimization techniques and it is concluded that particle swarm optimization has better performance compared to ant colony optimization for grid scheduling.