Assuming FreeSurfer reads the NIfTI SForm/QForm then the "img.nii" and "omg.nii" are identical (they are just stored to disk differently). The cropped image may segment better with FreeSurfer, but it really depends on the contrast of your T1 scan (e.g. fat suppression) and the amount of excess neck. In my limited experience, the segmentation of SPM12 is very robust, while the segmentation of FreeSurfer can be outstanding but depends very much on the quality of your T1 images. If you are just acquiring data now, I would suggest using the MGH multi-echo MP-RAGE sequence. The meninges and pial surfaces have different signal decay across the echoes, and FreeSurfer can leverage this information. Please look at the FreeSurfer support page for help with that tool.