Wiktor,
I cannot offer an exact explanation for such discrepancies. One possibility is a data precision issue; if so, add option "-datum float" to your 3dcalc command and see if that makes any difference.
A side note: you can use "3dmerge -1zscore ..." to the whole file, and it will convert all the statistics sub-bricks in the file to Z-stat (and keep anything else intact). At least it works for AFNI format. Not so sure about NIfTI files, though.
Gang