Due to the sparse structure of ultra-wideband (UWB) channels, compressive sensing (CS) is suitable for UWB channel estimation. Among various implementations of CS, the inclusion of Bayesian framework has shown potential to improve signal recovery as statistical information related to signal parameters is considered. In this paper, we study the channel estimation performance of Bayesian CS (BCS) for various UWB channel models and noise conditions. Specifically, we investigate the effects of (i) sparse structure of standardized IEEE 802.15.4a channel models, (ii) signal-to-noise ratio (SNR) regions, and (iii) number of measurements on the BCS channel estimation performance, and compare them to the results of -norm minimization based estimation, which is widely used for sparse channel estimation. We also provide a lower bound on mean-square error (MSE) for the biased BCS estimator and compare it with the MSE performance of implemented BCS estimator. Moreover, we study the computation efficiencies of BCS and -norm minimization in terms of computation time by making use of the big- notation. The study shows that BCS exhibits superior performance at higher SNR regions for adequate number of measurements and sparser channel models (e.g., CM-1 and CM-2). Based on the results of this study, the BCS method or the -norm minimization method can be preferred over the other one for different system implementation conditions.