Separate hotbox, I only use horizontal myself, but do have to maintain 2 vertical ones for my business partner.
Here is an example of a small foot print one that I am referring to.
http://www.landa.com/ViewCategories_Template3.aspx?Pid=1035
Everything, all the fuel tanks, pumps, engine, all fit under the burner and the width is no bigger then the burner. A PITA to work on these are with everything so close, but the foot print is smaller.
You can get a welder to put make a stand and put it up a few feet higher, but the goal when building the trucks are to keep the weight low, not put it up higher. Plus may of you guys try to keep everything low to fit into parkades, so putting a horizontal hotbox on stilts is not a solution for most. Vertical hotboxes you really don't want to raise due to their weight vs height, and typically once you put on a fuel tank of good size the footprint is 2/3 a horizontal one.
My experience is with both, I prefer them separate for trouble shooting and ease of maintenance though.
Look at John's big Ford
http://www.propowerwash.com/board/upload/attachment.php?attachmentid=17037&d=1305478440
Raise the single hot box 2 inches, change the dimensions of the fuel tank, ie double the height, half the length and move the battery and that big kohler could probably fit underneath. I have no exact dimensions, this is all an eyeball off a photo that he posted. Put that all under there and those two hose reels that are under the truck can fit where that engine was. Move the unloader and the valves on the base and put them on the burner frame and you can loose the red base and bolt the engine with rubber feet right to the truck.
Not worth the hassle for me to want to try, but combining the two in one foot print can and will save you space.