The 16 pins refers to the row of connectors on the LCD. The displays themselvces could be identaL, just one is already on a shield and the other isn't. There is no problem connecting the first to an Arduino, you could even mount it on a shield. The second is more convenient. I assume the second is more expensive but the extra $4 is well worth it, even if, like me, you never use the buttons.
Note that the bare display is the "standard" method and I believe it is implemented painlessly with the standard example given. The shield design of the second varies between manufacturers and there can be problems getting the connections right in the code. This is a problem that only happens once and should not be enough to deter you from getting it. It is just a matter of being forewarned and forearmed and you might ask the supplier about this.