Turbo code is recommended as a channel coding scheme, which has been shown to be capable of performing close to the Shannon Limit. In this paper, we compare the performance of both convolutional and block turbo codes over AWGN and Rayleigh fading channels. It is observed that the performance of convolutional turbo code is slightly better in the water fall region and the coding gain ranges from 0.5 to 0.7dB at BER of 10^-4 depending on the channel conditions. But below BER of 10^-4 or 10^-5 an error floor occurs in the case of convolutional turbo code. Block turbo codes tend to outperform convolutional turbo codes for low BER.