Generally speaking the 16ga was popular when there was a need for more than a 20 but less than a 12. With the new powders & propellants, the 20 has filled the place that was formerly occupied by the 16.

Good shots can drop geese & ducks with a 3" 20ga shells. If you're just starting out, I'd recommend a 12 over the 16. Hard to find shells = more $$ per box than for common sizes. I'd venture to guess that most 16 shells fired today are on sporting clay ranges.