Peter's suggestion to find out where you want to go to is a good one. Additionally, I think there are a couple issues that are confusing. First, a display program *could* do the equivalent of "3dWarp -card2oblique". That is, it could match the obliquity of some layer dataset to match the obliquity of another and display each voxel at the corresponding real location. Freesurfer might do that, and that may be why it looks okay there without going through the separate warping step. The afni GUI doesn't do that though. Instead the original data is shown as if it were acquired on the closest cardinal grid (RAI,LPI, LSA,...). Although the voxel sizes are right, the absolute x,y,z locations are not the true ones. The original locations are rarely used or even useful, so that's usually not too bad, but it can be confusing.

The NIFTI datasets keep all the information about the orientation and obliquity in either the sform_code or the qform_code, so that's probably where freesurfer is getting that information. Once all datasets are aligned, you may want to remove any obliquity information from the header and assume the nearest cardinal orientation grid. That operation is done with "3drefit -deoblique" and should be applied only to those datasets that are aligned, and you are certain you will not need that information for future processing. I suspect that a similar procedure is done here on the Connectome data for similar reasons:

https://wiki.xnat.org/pages/viewpage.action?pageId=15171618