Speaker direction finding techniques have aroused interests due to achieving the capability of receiving high-quality dis- tant signals. Interesting concepts can be achieved through the comparison of such techniques whereby importance is in achieving high quality signals at reasonable complexity rates. With this aim in mind, this paper presents a critical compari- son between two such traditional techniques; Time-Difference of Arrival (TDOA) estimation by Generalized Cross Correla- tion (GCC) and space scanning by Steered Response Power (SRP) of a beamformer. Each is analyzed under diverse con- ditions of noise and reverberation. Simulation results and experiments based on real data have been able to show that SRP with short data segments and due to its characteristic of averaging over the spatial dimension illustrate better accuracy results than that of GCC. These results have instigated a new method in the estimation of the source direction from a set of TDOAs based on spatial curvature collision. This paper dis- cusses how this procedure reduces the computational cost more than 50 times compared to the conventional method of Root Mean Square (RMS) error minimization over the candi- date locations.