Bill, being those drivers you mentioned are constant current drivers, the actual cell(s) used will determine the current draw. Without knowing the battery(ies) being used, we can't really estimate battery current draw to answer your question.
I do have a 5W (WX1T) with a DB1000 in an LED module for a SureFire M4 Turbo Head (look at my avatar!) and it can work with 2 rechargable cells (barelly), 3, or 4 (absolute maximum!). As you can expect, the current draw gets smaller the more cells I use. I don't have numbers here in front of me at the moment but I "think" it was around 350-400mA with the 4 cells
Will