In this paper, we analyze the levels of performance of the (full or reduced versions of) space-time adaptive processing (STAP) algorithms applied to high-frequency surface wave radars (HFSWRs) for marine target detection to verify whether this family outperforms the usual moving target indication (MTI) algorithms. In fact, STAP algorithms have well-known drawbacks (e.g., large amount of secondary data). The propagation and backscattering of radar signals are included in the covariance matrix calculation. Since the propagation and backscattering have to be derived from physical features of the sea (e.g., sea Doppler) and the atmosphere, we also include the difference induced by the waveform (pulsed radar/chirp) in our study. Moreover, since the inverse covariance matrix is used in the target detection algorithms, matrix conditioning is also inspected for practical implementation reasons. We numerically detail the performance (signal noise clutter ratio and conditioning number of the STAP algorithms) with regards to the MTI performance for several configurations of radar and sea state. These results show that the improvements of signal noise clutter ratio are counterbalanced by a raise of the conditioning number, except in the case of eigencanceler approach. The sea-state parameters have few effects on the performance unlike to radar parameters.