Most People Prefer Right Ear for Listening

A well-known asymmetry in humans is the right ear dominance for listening to verbal stimuli, which is thought to reflect the brain's left hemisphere superiority for processing verbal information. This preference for hearing with the right ear is also found in rats, Japanese macaques, harpy eagles, sea lions and dogs.

However, the left ear (and right brain) excels at picking up emotional cues. When it comes to music, pitch, timbre and loudness are discriminated better with left ear (right hemisphere), but duration is better discriminated with the right ear (left hemisphere).

These findings may explain why people are not entirely satisfied when using hearing aids for only one ear. Ideally, BOTH ears should be aided. BUT, if one had to choose between two equally deaf ears, the right ear would be the preferred side.

Reference:
Side biases in humans (Homo sapiens): three ecological studies on hemispheric asymmetries. Naturwissenschaften September 2009, Volume 96, Issue 9, pp 1099-1106