This paper exhaustively discusses and compares the performance differences between radial basis probabilistic neural networks (RBPNN) and radial basis function neural networks (RBFNN). It is proved that, the RBPNN is better than the RBFNN, in the following several aspects: the contribution of the hidden center vectors to the outputs of the neural networks, the training and testing speed, the pattern classification capability, and the noises toleration. Finally, two experimental results show that our theoretical analyses are completely correct.