The term bottleneck really does get thrown around too much. You are clearly CPU bound though.
In games like H1Z1 or Planetside 2 or Blade and Soul, you'd be pinning your CPU at 100% with your GPU lazing around 28-35% usage. BF4 and Rust also very heavily CPU-bound, not as badly as Planetside 2, but still, I'm not surprised you're pinning your CPU at 100% load, screaming for help. You're getting the same FPS with the 1070 as you did with the 970 because the CPU is responsible for sending the information to the GPU so it can draw the frames you see on your screen. If your CPU can only push information so fast, you'll get the same framerate regardless of headroom, and that's determined by anything from clock speed to IPC to the game engine itself. Rust is not well optimized by any definition of the word.
Idle usage at 10% is on the high side, so check your background processes for abnormalities and unnecessary programs. Windows Defender can also be at fault for high CPU usage all across the board, which is why I like to disable/uninstall it (I fully uninstalled mine, works wonders).