PC, upgrading/current status help?

First off, here are my current specs: 

AMD Athlon II x4 650 3.2GHz

XFX Radeon HD 6770 1GB 128-bit GDDR5

6GB DDR3 RAM (CPU-Z says 2000MHz, but I call BS)

CORSAIR Builder Series CX600 V2 600W

Now, most of the games I play I can near max out; like BLR, MechWarrior Online, War Z, LoL, not quite Skyrim, and some other less popular titles. My problem is that in a couple of my games, I can barley play on low. Those being PlanetSide 2, and DayZ. Does the problem lie with my CPU? I already planned on upgrading it, or is it my GPU? I've been told and for the most part experienced the 6770 being a great card in general. Could it be these games have poor optimization? My PC was a Lenovo that I bought and put in a new PSU and GPU, as I wanted to try some gaming on PC. I'm going to build a new PC, but I'm going to re-use my PSU, GPU, and HDD for a while to save some money, just a quick overview of my future build; Phenom II x4 965, 8GB 1866MHz RAM, Gigabyte GA-970A-D3, and of course re-using my GPU, and PSU. Thanks for any info!

 

Here is a benchmark between your Athlon and a phenom II 965 at stock clocks, look for the 3 games benchmarked and noticed the fps difference is roughly 10fps-15fps. http://www.anandtech.com/bench/Product/188?vs=102

I honestly think its a combo of both your cpu and gpu, your athlon is just those few fps then a phenom add the few less fps from your gaphics cards and issues. Do you have the latest drivers on your 6770?

I would just upgrade you videocard to 7850. 

If you're going to upgrade motherboard and cpu, might as well save up a bit and go for an Intel core i5 build.  It'll last for quite some time and the next generation of video cards are on the horizon so that may push the radeon7000/geforce600 series cards down in price.

If you purchased a video card first, you're probably not going to see much of a price drop on cpus later down the road.