I've used both and basically the D800 requires nearly double the shutter speed for me. This is with the same lens and subject when shooting at the same time side by side. Part of it is Sensor MegaPixels but mostly due to the camera size, weight, and AF speed. Yes the D4 is faster and not just frame rate. However, the D4 is to heavy to shoot at Events for 8 hours and too expensive for me.
So,I shoot Landscapes and Sports handheld with the D800 and usually a 28-300 lens. Auto ISO settings are currently 100, ON, 6400, and 1/640. Sometimes I bump the speed to 1/800s for Sports. I am enjoying the highest keeper rate ever after considerable improvement in my hand holding technique.