This paper analyzes the performance of systems with dual-polarized antennas in correlated Nakagami-m fading channels as a function of envelope correlation and cross-polarization discrimination by means of the characteristic function of the instantaneous post-maximal ratio combining (MRC) signal-to-noise ratio (SNR). Systems of interest include systems with receive polarization diversity and systems with transmit and receive polarization diversity employing Alamouti space-time code. The expressions for the average symbol error probability as a function of SNR assuming no power control, and the expressions for the average required transmit power to achieve the constant desired post-MRC SNR assuming perfect fast power control, are derived. Finally, a comparison between analytical and simulation results is used to validate the analysis.