Simply put, absolute pitch is more subtle and accurate.
With relative pitch, there are twelve major chords. With absolute pitch, there is only one C major chord. The distinctions you can make with absolute pitch are finer and smaller. And each note has its own sound. Transpose a Beethoven symphony into another key and it doesn’t have the same feeling anymore. Each key has its own mood.
With a more refined ear, you have more precise options to help you make the right musical decisions.