It's a good question. One would have to examine the details of the equations utilized, which can be found on Github. The ZAF.BAS routine contains the source code for all the corrections:
https://probesoftware.com/smf/index.php?topic=570.0In general one can only say that the Heinrich-Duncumb-Reed method is an older ZAF type correction that is quite different from the more modern PAP phi-rho-Z method which combines the absorption and atomic number corrections. Realistically one should combine the absorption and atomic number corrections in HDR and compare those combined absorption and atomic number correction values in the PAP method. Of course just because a method is newer doesn't mean that it's better... it depends on the compositions involved.
That's because, the largest differences in these two methods are probably the standard materials utilized to "tune" these the equations at the time they were created. PAP used the POUCHOU.DAT and POUCHOU2.DAT k-ratio databases (provided with CalcZAF and found in the CalcZAFDATData folder), while the HDR method probably utilized a different k-ratio database (I'm not sure which, but it could have been the NISTBIN.DAT k-ratio database which is also found in the CalcZAFDATData folder).
You might want to contact Brian Joy at Queens University as he has looked into these equations in some detail.
My final comment is that with high atomic number materials like this, the backscatter correction can be quite large and because current backscatter corrections are improperly based on mass concentrations, there are significant errors associated with them in some compounds. This is the motivation behind our recent paper:
https://probesoftware.com/smf/index.php?topic=1111.msg11954#msg11954And we are working on implementing a new backscatter correction in CalcZAF/PFE as I write this. You might want to look at the A/Z ratios of the elements in this material and see how different they are. The more difference in the elemental A/Z ratios in a compound, the larger the mass bias effects in the backscatter correction.