How bad of a bottleneck is this cpu on my gpu

Thats a quite old cpu, have you checked your cpu/gou usage in game? you can use msi afterburner to see the usage of each core, if your gpu is not reaching 90-100%, you have a bottleneck.

Yup, that CPU is bottlenecking your GPU almost for certain. A 8350 will help but not by much. The real difference will occur when you switch to an Intel CPU. The difference will be very surprising going from Phenom II X4 840 to an i5-4690K, especially if you overclock the 4690K to 4.5+Ghz. Depending on how bad your CPU bottleneck was, it is likely you'll see almost double the FPS with the same GPU.

I beg to differ there, while the 4690k is superior to a 8350, he is only using a 270X, and there will be not a significant difference between the two CPUs that justifies getting a new board and a more expensive CPU, he'd be spending like $200-$300 bucks more only to get 2-3 more FPS with that card.

Already moving from an 6-core FX-6100 to an i5-4670K nets you double the FPS with the R9 290x in COD:AW :


Going from Phenom II Quad to an i5-4670K will definitely net you a lot more than 2-3 FPS with the 270X. A lot more.

I highly recommend this upgrade and would be very interested in your results.

PASSMARK single thread scores are very useful:

Phenom II X4 965:
1193

FX-8350:
1509

i5-4690K:
2240

Analysis:
Roughly speaking, this score (if four or more cores) tells you the frame rate difference at the point of total CPU bottleneck. Thus, if you upgraded to the FX-8350 and it still remained a CPU bottleneck you would gain at most an improvement of:

26% (1509/1193)

If we compare the i5-4690K by the same logic we get:
87%

Again, these represent completely CPU bottlenecked scenarios but it's a good indication of relative performance. Put another way the i5-4690K is about 48% faster than the FX-8350 on a per core basis. The FX-8350 has more cores but more than four are rarely used (fully).

Summary:
Not sure what to say here. The FX-8350 isn't a huge upgrade for games that can't use more than four cores. The Intel CPU however is but it needs a motherboard obviously and possibly a new copy of Windows of you don't own Windows 8.

*If you've got pretty bad stutter then I don't think the FX-8350 is going to make a lot of difference. Rather, it may be the game itself so a future PATCH may help: http://segmentnext.com/2014/11/03/call-of-duty-advanced-warfare-crashes-low-fps-errors-graphics-performance-stuttering-and-textures-fixes/

More info: http://www.dsogaming.com/pc-performance-analyses/call-of-duty-advanced-warfare-pc-performance-analysis/

*Photonboy's analysis of the above link:
The i7 uses 23% (six-core) so we can compare to the X4-965 like this using Passmark scores:

i7-4930K-> 0.23 X 13132 = 3020

X4-965-> 4271

This is a weird way to do it but it appears like your CPU should be able to handle this game fairly well. Thus, I'm pretty sure getting a better CPU won't make much difference on your average frame rate. Again, I think it's a software issue with the game, or possibly drivers.

As for the link above also note:

"In order to find out whether this title can be played with constant 60fps on a variety of PC systems, we simulated a dual-core, a tri-core and a quad-core system. All of the aforementioned systems were able to push constant 60fps. However, we do have to note that on our simulated dual-core system there was noticeable stuttering issues that went away as soon as we enabled Hyper Threading. Owners of really old dual-core CPUs may be able to overcome those stuttering issues by overclocking their CPUs..."

Sorry my above post ended up quite long. My main point is that his stuttering doesn't seem to be a CPU issue. Please either read fully or jump to my last LINK which tests the game's CPU performance.

Specifically the last PARAGRAPH above.

Or just read this:
"Quite frankly, the minimum PC requirements are spot on. A dual-core CPU is enough for this latest COD game... "

Yeah that's a huge CPU bottleneck