Question 1600 OR 1866

For gaming systems, there are plenty of legitimate reviews from the DDR3 era showing very little difference in performance between 1600mhz and 1866mhz memory usage. In fact, it's doubtful you'd notice the difference in any meaningful way. Adding MORE memory though, that MIGHT bring some improvements depending on the game, your settings, and the resolution you are gaming at. It's likely that many games may begin recommending 16GB as a minimum, and in fact some already have.

Also, it looks to me, despite what the Crucial website might say, that the motherboard used in those systems only supports memory speeds up to 1600mhz, although there can be discrepancies in some of the specifications since often they are not updated yet newer BIOS revisions often bring support for hardware and upgrades that weren't specifically supported at release.

Likely, you can use either and I'd go with whichever speed was available at the lower price, all other things being equal. If it's not supported it will simply default to the lower speed.