High-accuracy angle of arrival (AoA) and angle of departure (AoD) estimation is critical for cell search, stable communications and positioning in millimeter wave (mmWave) cellular systems. Moreover, the design of low-complexity AoA/AoD estimation algorithms is also of major importance in the deployment of practical systems to enable a fast and resource-efficient computation of beamforming weights. Parametric mmWave channel estimation allows to describe the channel matrix as a combination of direction-dependent signal paths, exploiting the sparse characteristics of mmWave channels. In this context, a fast Transformed Spatial Domain Channel Estimation (TSDCE) algorithm was recently proposed to perform parametric channel estimation with low complexity, which in turn results in a full characterization of the transmitting and receiving angles for dominant signal paths. In this paper, we analyze the AoA/AoD estimation capability and accuracy of the TSDCE algorithm in detail. We find that the TSDCE algorithm has a significant performance advantage with respect to the traditional approach, which is based on frequency domain processing, in complexity-constrained environments, especially at high signal-to-noise ratios.