The best way to find out if the two procedures would give very different principal eigenvectors would be to try BOTH methods on one dataset and see what happens.
The results will be at least different a little, because of the resampling going from +orig to +tlrc space. However, my guess is that the results for the principal eigenvector will not be significantly different, since this is a form of averaging. However, lower eigenvectors would probably be more affected.
You can use the AFNI program 1dsvd to compute eigenvalues and eigenvectors of column vectors, by the way.