Knowledge of how executive functions relate to preferred hearing aid (HA) processing is sparse and seemingly inconsistent with related knowledge for speech recognition outcomes. This study thus aimed to find out if (1) performance on a measure of reading span (RS) is related to preferred binaural noise reduction (NR) strength, (2) similar relations exist for two different, non-verbal measures of executive function, (3) pure-tone average hearing loss (PTA), signal-to-noise ratio (SNR), and microphone directionality (DIR) also influence preferred NR strength, and (4) preference and speech recognition outcomes are similar. Sixty elderly HA users took part. Six HA conditions consisting of omnidirectional or cardioid microphones followed by inactive, moderate, or strong binaural NR as well as linear amplification were tested. Outcome was assessed at fixed SNRs using headphone simulations of a frontal target talker in a busy cafeteria. Analyses showed positive effects of active NR and DIR on preference, and negative and positive effects of, respectively, strong NR and DIR on speech recognition. Also, while moderate NR was the most preferred NR setting overall, preference for strong NR increased with SNR. No relation between RS and preference was found. However, larger PTA was related to weaker preference for inactive NR and stronger preference for strong NR for both microphone modes. Equivalent (but weaker) relations between worse performance on one non-verbal measure of executive function and the HA conditions without DIR were found. For speech recognition, there were relations between HA condition, PTA, and RS, but their pattern differed from that for preference. Altogether, these results indicate that, while moderate NR works well in general, a notable proportion of HA users prefer stronger NR. Furthermore, PTA and executive functions can account for some of the variability in preference for, and speech recognition with, different binaural NR and DIR settings.