Just reading through this thread I had to give some impressions I have had by using both my Intel rigs and AMD rigs.
For reference I have 4 rigs I use daily, which consist of the following. Intel I5 2500k, Intel I7 4770k, AMD Fx 8350/6300 and AMD 955 Be. The GPU's I have and swap around from rig to rig are ATi 5850, Nvidia GTX 580, GTX 670 and GTX 780.
I play mainly FPS games, BFBC2, BF3 and BF4 all at 1920*1080p. When playing these games on any of the rigs above the only one I do notice a difference on is the 955 Be. The rest of the rigs play the games exactly the same, yes when using Fraps the Intels get a few FPS more while gaming but visually while playing I do not see or feel a difference. If a game is more dependent on the Cpu and/or you are running a pair of Gpu's in SLI or XFire you will see a significant difference when running a Intel chip over an AMD.
If your main plan for the rig is gaming then the Fx 63xx is the way to go, it will be easier to OC because it doesn't have as much power draw as the Fx 83xx when overclocking, therefore less heat to dissipate. If it is possible for you to cancel the Fx 4xxx you purchased and replace it with the Fx 63xx, I feel that would be a wise decision. A Gigabyte 970 UD3 board coupled with the Fx 63xx chip and a R9 280X or better gpu will be a good gaming rig.