In this study, the advantages of Digital Signal Processing (DSP) hardware for hearing aids are investigated in the context of multiple microphone arrays. One key question in multiple microphone DSP system design remains the allocation of processing resources between the number of microphones and the number of adjustable tap weights applied to each microphone. This study addresses the appropriate distribution of these resources for currently implementable adaptive DSP systems. Comparisons are made by computer simulation that includes acoustic headshadow, reverberation effects and non-ideal microphone array hardware in a wide variety of environments. Variations in the number of interfering sources, the amount of reverberation and the microphone array configuration leads to several important conclusions. Performance improvements provided by the processors are reported as the broadband unweighted signal-to-babble ratio of pre-emphasized speech and speech-shaped babble. Results are demonstrated for both fixed and robust adaptive systems.