Matching arc flow accumulation with whitebox

[Michael Lefsky]

I want to move our watershed analyses from esri products to whitebox. My first comparison of the output of each package's flow accumulation algorithm indicated that whitebox gets close to what esri produces. Still, there are differences and I'd like to demonstrate that whitebox can better correspond with the output produced by esri before adopting whitebox. 

Does anyone have experience with this type of comparison or have an analysis of why results will differ between the two software packages?             

Thanks in advance for any help you can provide.

Michael