To answer your question.
If you are playing a CPU heavy game, the i5 would do better.
If you're playing a game with detailed graphics that maxes out the GPU then you wouldn't see a difference.
My favorite types of games would bottleneck both those CPUs in that setup.
.
But, to try to explain a few things for you:
If you just Googled "i3 4440 vs amd kaveri a10 7860k" you can see the performance difference. Basically saying the i5 is 30% - 40% faster.
http://www.cpu-world.com/Compare/453/AMD_A10-Series_A10-7850K_vs_Intel_Core_i5_i5-4440.html
A bottleneck is the part the system is waiting on. When you load a game, it's the hard drive. When a game has complex mechanics (like a RTS) it can be the CPU. When the game has fancy graphics (like a FPS), it will probably be the GPU.
So, you'll only see a difference if you're playing a game that is waiting on the CPU and isn't fully using the GPU. You can use tools like GPU-Z to watch your GPU usage.