16bit color has 65536 possible colors, while 24 bit has millions and 32 bit has billions.
I like using 24bit color, because it allows all RGB combinations of color. With 16 bit, the computer will render 0/0/0 (black) and 0/0/1 as the same. Of course, as you noted, your eye cannot tell the difference between these.
(People with good can recognize more than 65,000 colors, but no-one can recognize all the 24-bit combinations.)
If your machine has a 24-bit setting, try it. If not, live with 16-bit ... since the higher level degrades performance.