Im not trained, but have played for many years and I believe it does make a difference, but with any given song you have to decide what sounds right over what is easy play play.
An example , I've been listening to versions of whats going on covered by Paul Carrack, the bass player plays around a bit with it and it sounds truly amazing, but various parts sound obviously different to the original and not just due to the modern strings and pickups, you can hear where he is on the fretboard.
So yes, they do sound different, and it only matters if you dislike a sound, or you need to play a certain fret because its more fluid in where you are moving to next.