ninjanafi :
I don't know the meaning or difference between g-sync or freesync.
Here is my PC Build, I have 16 GB RAM in my plan cause I plan on playing really AAA titles like GTA V< Fallout 4, CSGO, whatever really
https://pcpartpicker.com/list/CVgfFt
gsync and freesync are technology built into monitors that sync the GPU with it. gsync is specific to nVidia, with expensive monitors and freesync is for AMD cards and the monitors are much cheaper as there is no special hardware. If you are running a standard monitor, then you can ignore all this.(If the monitor description doesn't specify gsync or freesync, then it's a standard monitor.)
You have 16gb RAM, the other poster was referring to VRAM (I assume). They are separate and independent, but with 6gb or 8gb, you will be fine for now and the near future. I haven't seen a game use that much yet.
You will be happy with either card, the 580 has a small performance advantage and in this case, price advantage.