You can't se the difference between the two formats most of the time on the computer displays as the computer display cards are 8 bit per color, but the differences are there and do come into play during editing and post processing you images, included printing to your printer.
Print services if they will take 16 bit color depth files only then would you be able to tell the difference but most will not be able to see it.
Attached are 4 images with different color depths, two any one will be able to tell the difference and two are close in color depth.
Between 1 and 2 which one is the original (no peeking at the file names )