The 3dAFNItoNIFTI program and other AFNI programs that read afni format data and write NIFTI format keep all the AFNI header data in a private field, so nothing should be "lost" as far as AFNI is concerned. However, other non-AFNI programs will not be able to read that information and probably will not write it out either.
If you use the 3dAFNItoNIFTI program with the -pure option, the AFNI extension is not written out. Some differences that are lost (ignoring the AFNI extension) are multiple scale factors for short integer data (not available in NIFTI), history, notes, ID codes, rotation and warping transformation history, links to anatomical parent datasets for talairach type transformation.
You can use the commands nifti_tool to display NIFTI header information and remove or add AFNI extensions into a NIFTI file. Use 3dinfo and 3dAttribute to display AFNI header information. Most AFNI programs read and write NIFTI and AFNI brick format data.