The best CPU you can get for Dolphin is a 4670K. An i7 brings no benefits.
Manually overclock yours. You'll get better OC results and Dolphin performance if you manage to get a higher clock.
The CPU is usually the bottleneck, but you also need an adequate GPU if you want to render at such a high resolution.
What GPU do you have?
EVGA GTX 780 Ti SC, have it clocked at 1300 core / 1575 mem @ 1.212v, 21 C idle / 55 C load.
What I found during testing was that my ability to run higher resolutions/IQ was, for some reason, directly tied to CPU performance. The game wasn't even utilizing the card at its full potential under stock clocks, floated around 60-70% usage, and setting it to performance mode for Dolphin (forcing max clocks) under nVidia control panel didn't make a difference.
When I did manage to get a 4.4ghz overclock (unstable, I am convinced I wasn't overclocking correctly), the performance in certain areas where the game stutters @ 4.2ghz certainly improved.
So yah...certainly CPU related it seems? I just need a really good Asus/Haswell overclocking guide. Last time I overclocked was in the P4 days, and boy was it easier back then.
Edit: And to clarify, I only have stutters under very specific, extremely graphically intensive scenes. Such as ability animations/heavy combat sequences. I've tested the problem by stating a Chain Attack sequence where it will stutter and be paused at the same time (waiting for input for next move), and then lowering the graphical settings on the fly. The stutter goes away with lower settings.
Also, the area right before Frontier Village is particularly hard on the CPU, it seems. Even if the rest of the game before that is fine, I always have issues/have to lower IQ there. Must have to do with the really dense vegetation or something.