The difference is that the output doesn't have the full oblique information as the base dataset. If the grid is exactly the same, you may copy the obliquity attribute to the warped dataset. Otherwise, you can remove the obliquity from the base dataset (or preferably a copy of the base dataset), and all should be good.
3dcopy mydset.nii myafnidset+orig
3drefit -atrcopy myafnidset+orig IJK_TO_DICOM_REAL mywarpeddset+orig
or
3dcopy mydset.nii myafnidset+orig
3drefit -deoblique myafnidset+orig