#1 Make sure your CPU isn't overheating. 
- You will need prime95 to stress your CPU. Run Small FFT test.
- You will need coretemp to check your CPU temps while stress testing.
 
#2 Perform a clean boot of windows. 
- Instructions on how to perform a clean boot of windows can be found HERE.
 
#3 Perform a clean installation of video drivers.

1. Uninstall Precision X/Afterburner if installed, make sure to select "no" to saving profiles when asked. Reboot the machine.
2. Download & save 337.50 driver to your desktop. 
3. Double click on 337.50-desktop-win8-win7-winvista-64bit-english-beta.exe located on your desktop & run the extractor.
4. Select custom advanced install, under custom installation options uncheck all options but graphics driver & physx system software, if you are using audio over HDMI please select the HD Audio driver, if you have a 3D capable monitor and would like to use 3D at some point select the 3D Vision driver also, check mark perform clean install, then click next to install the driver, reboot when asked.
5. Re-install Precision X/Afterburner if you want, do not install both choose one or the other.

 
#4 Test PC and report back.

BF4 still running like junk?

Why you test with Passmark.
Gaming Performance you will best to see in Unigine Heaven 4.0 and Firestrike Xtreme.
 

Even at 4.0GHZ your AMD processor will have a bit of a CPU bottleneck. There are many forum members who have had problems with both BF3 and BF4 and there are some threads in the gaming forums which should help you. In other games like Crysis 3 for example what is the performance there?

My CPU usage is never capping.  It does not go above 60% range in BF4.  When I get a frame drop, the cpu usage drops at the same time the frame rate drops.  It drops from around 60% to 20%.  In the DirectX 9 Complex passmark test my framerate is always 29-32 fps and the cpu usage never goes above 5%.
 

 
If someone could also run a benchmark and post their results that would be great.

I ran the same test with Passmark for you to compare to.  This is with my 780Ti  SC at stock clocks.
 

Vlada011
But somehow you don'w want Unigine Heaven 4.0, Firestrike and 3DMark11, you don't need to buy test or register, only finish and present even on Performance. 
Tell me settings for 3D Tests, resolution, etc...
DX11, 1920x1080, AAx8, 400 Giant Space Jellyfish...???

I'm working on it.  3DMark 11(Extreme Preset):
 

 
 Looks Normal.
Rest to come.  Also, thanks for the passmark bench.

 
http://imgur.com/sAsOoOb
 
Graphic 3D Compute is 5338.
 
But this results I don't know how they could present exactly power of GPU, OK some test pull max power target from Graphic but resolution in some tests is low. In such test CPU, RAM speed can make decision too. OK graphic card boost constant on 1202MHz but...
On one moment I saw 120% power target...

Rwkeith your 3DMark11 GPU score is completely normal for your card.
But you see difference with Intel CPU
 

 
Note: I back CPU clock on 3.9GHz because now I can't risk with anything before Haswell E is launched, I don't want to stay with PC few months or to borrow money for 4770K and than miss 5930K. Because this is not exactly my best score, and last BETA driver I saw little drop in results test compare with previous WHQL driver, but I use for gaming and when Haswell E show up before upgrade I will OC system.
 
But that's small result for Unigine Heaven, that's result of GTX780 SC or Classy, maybe because CPU.
I will try to search to compare GTX780Ti on 8350.
Don't look my 3DMark 11 GPU Score because graphic is overclocked, but you see even Intel on stock increase X score.
I would love to try your card on my comp to check, but that's impossible.
Anyway recommendation of anybody would be to try in some PC with i7 2nd, 3rd or 4th generation if you want to know is it graphic card OK.
If your result in Unigine Heaven is same on Intel i7 CPU that would be normal reason for RMA. 

You can upload result as me, with link where someone can click and check in higher resolution.
You result is even CIA impossible to decode to become visible even if that is question of existence. 

Rwkeith
Okay, I found the eluding problem.  After going to install my old card, I noticed that my card was sticking out halfway in the PCI slot!  Now I am getting much higher frames in the tests.  

Nice find. 

Here's the 3DMark test again.  I also added a bit of overclock 35 to baseclock, 300 to memclock:
 

 
I'm pretty convinced now that my card is not at fault now.  Maybe I'll see about overclocking my CPU.  For now, I'll see how much overclock I can get from my card.

Vlada011
SUPER! That's nice, You have nice score for GTX780Ti SC.
You see everything is OK. Enjoy in games. Leave benchmark tests. 
That's ACX model?

Yes, and thanks for your help.  I wasn't aware the cpu would make that big of a difference, but I suppose I'll eventually have to go intel.

If you have money for upgrade you could easy choose some Intel i7 and new motherboard.
Z97 will be compatible with 4770k/4970k and Broadwell CPU and for few months
Haswell Extreme will show up with some completely new features in IT world.

It's CPU, they measure speed usually when all cores work and games use 2-3-4, and speed per core is slow compare to Intel. 
AMD compensate that with many cores but only in application where usage is 100% of all cores.