The problem of computing the Betweenness Centrality (BC) is important in analyzing graphs in many practical applications like social networks, biological networks, transportation networks, electrical circuits, etc. Since this problem is computation intensive, researchers have been developing algorithms using high performance computing resources like supercomputers, clusters, and Graphics Processing Units (GPUs). Current GPU algorithms for computing BC employ Brandes' sequential algorithm with different trade-offs for thread scheduling, data structures, and atomic operations. In this paper, we study three GPU algorithms for computing BC of unweighted, directed, scale-free networks. We discuss and measure the trade-offs of their design choices about balanced thread scheduling, atomic operations, synchronizations and latency hiding. Our program is written in NVIDIA CUDA C and was tested on an NVIDIA Tesla M2050 GPU.