Besides being a much more rugged body ("workhorse" as PSAGuy stated above), the D4 has a much deeper buffer, a much higher frame rate which impacts the mechanical design of the shutter and mirror mechanism, a built in portrait grip, and a much bigger battery.
Because of all these differences from the D800, the D4 is intended for a much smaller market. This means that Nikon has to amortize their development and engineering costs over much a smaller number of units. This too adds significantly to the selling price.
I have both a D4 and a D800e. I can't decide which I like best. I use them for different things. The D4 is the high ISO and high frame rate champ and its 16Mp is already overkill for computer presentation and portraits. The D800e is obviously the high resolution champ and fantastic for making large landscape prints.
Gary in SE Michigan, USA. Nikonians membership - My most important photographic investment, after the camera. D4, D810, D300 (720nm IR conversion), D90, F6, FM3a (black), FM2n (chrome) YashicaMat 124, Graflex Speed Graphic 4x5 My Nikonians Gallery & Our Chapter Gallery