When we create our arrangements, we strictly adhere to the original recording in matters of harmony to create a faithful reproduction. When we produce arrangements in alternate keys, we may have to make subtle adjustments to the notes of certain instruments or the voicings for groups of instruments.
For example, a bass guitar (4 string) has a lowest note of an E natural. If the original contains a bass part favouring the low E (common practice in many pop songs), when a version in a lower pitch is produced, we may need to transpose some notes up an octave. Our ears are used to hearing the song in its original key so when certain notes are changed, we can perceive that something isn’t quite right.
When we have to make these changes, we do so in the most musical way possible and by the smallest intervals we can.