Beyond hearing loss compensation, hearing systems must address environmental noise. This paper proposes a binaural hearing system comprising of a wide dynamic range compression (WDRC) and a deep neural network-based noise reduction (DNN-NR) as major system components. The WDRC in turn consists of an audiogram-based NAL-R gain rule and compression parameters tailored to hearing-impaired listener’s residual dynamic range. The system inherently preserves binaural cues by maintaining a common gain throughout. Another contribution of the paper is the disentanglement of the effects of individual system components on output segmental SNR (segSNR), hearing-aid speech intelligibility (HASPI), and hearing-aid speech quality (HASQI) metrics. To address the lack of a suitable reference signal for SNR analysis in the compressed hearing domain, we here introduce a shadow-filtering approach in parallel to the main processing path. Our study is limited to an investigation of a single standard hearing loss audiogram, representative of generic consumer hearing systems.