A signal processing approach combining beamforming with mask-informed speech enhancement was assessed by measuring sentence recognition in listeners with mild-to-moderate hearing impairment in adverse listening conditions that simulated the output of behind-the-ear hearing aids in a noisy classroom. Two types of beamforming were compared: binaural, with the two microphones of each aid treated as a single array, and bilateral, where independent left and right beamformers were derived. Binaural beamforming produces a narrower beam, maximising improvement in signal-to-noise ratio (SNR), but eliminates the spatial diversity that is preserved in bilateral beamforming. Each beamformer type was optimised for the true target position and implemented with and without additional speech enhancement in which spectral features extracted from the beamformer output were passed to a deep neural network trained to identify time-frequency regions dominated by target speech. Additional conditions comprising binaural beamforming combined with speech enhancement implemented using Wiener filtering or modulation-domain Kalman filtering were tested in normally-hearing (NH) listeners. Both beamformer types gave substantial improvements relative to no processing, with significantly greater benefit for binaural beamforming. Performance with additional mask-informed enhancement was poorer than with beamforming alone, for both beamformer types and both listener groups. In NH listeners the addition of mask-informed enhancement produced significantly poorer performance than both other forms of enhancement, neither of which differed from the beamformer alone. In summary, the additional improvement in SNR provided by binaural beamforming appeared to outweigh loss of spatial information, while speech understanding was not further improved by the mask-informed enhancement method implemented here.