Details regarding the how dcm2niix handles diffusion vectors is described here. The wiki includes sample datasets from each vendor, and links to a dedicated document that  describes how you can validate the generated vectors. 

I should note that all the gradient tables I have seen are specified as "CoordinateSystem = xyz" (with respect to scanner bore), rather than using phase, readout and slice directions (and in my experience, this is the frame of reference used to report the gradient directions in the DICOMs). Therefore, I would suggest carefully following the dedicated document to confirm the solution and generating an issue on the dcm2niix GitHub page if there are issues. I suspect all is well and the difference is in the direction of your prs phase-readout-slice coordinates to the ijk column-row-slice coordinates expected by FSL. As ever, recall that DICOM coordinates and NIfTI coordinates differ.  Therefore, dcm2niix expects Siemens to report vectors with respect to the scanner bore, and it must generate vectors in FSL format that is with respect to the image slices. 

The image orientation and vector direction expected by FSL are unusual, as described here and here. But dcm2niix's siemensPhilipsCorrectBvecs() function has provided robust FSL results with the validation datasets I acquired (provided on the dcm2niix wiki).