AFNI dataset files (.HEAD/.BRIK pairs) should be completely portable between UNIX systems. The .HEAD file is ASCII text, and the .BRIK file is binary. The byte order of the .BRIK file is stored in the .HEAD file, and AFNI programs will byte swap on input, if needed.
Other files you might generate with AFNI programs -- or other un-named packages -- (ANALYZE .hdr/.img files, MINC .mnc files, .1D files) are also portable.
bob cox