In this paper we compare the performance of cyclic prefix based OFDM (CP-OFDM) systems and OFDM/offset QAM (OFDM/OQAM) systems in doubly dispersive channels, by investigating the signal reconstruction perfectness, time and frequency dispersion robustness, and sensitivity to frequency offset. Both analysis and simulation results show that various parameter adaptations can be made with respect to the channel state information to improve the system performance.