Than the FSL FAQ seems to be a bit confusing about this.

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FAQ.6
How can I modify the left/right or "radiological"/"neurological" ordering of
my data?

When it is absolutely necessary, there are two ways to modify the
orientation of a nifti image. Note, however, that these operations easily
lead to confusion about which side of an image is left or right. Therefore,
use with caution. The most appropriate place to use these tools is: (1) in
the initial reconstruction of images (where it may be necessary to force the
correct orientation (or change the data ordering); (2) to convert
"neurologically" ordered data into "radiological" order for further
processing in FSL (this is our strong recommendation); or (3) to correct for
poor converters or to suit the user's preference.

In order to use the FSL tools to convert "neurologically" ordered data into
the "radiologically" ordered format for use with the current version of FSL
(3.3) the following commands should be run:
fslswapdim input -x y z output
fslorient -swaporient output

This will create a new image (output) which has the opposite left-right
ordering as the input image. That is, if the input image was
"neurologically" ordered, the output will be "radiologically" ordered. This
assumes that the original orientation information in the input image is set
correctly. If these commands are used on Analyze images, or nifti images
where neither qform or sform are set, then the fslorient command will not
change anything, but the underlying data will be changed by fslswapdim and
the left-right orientation will still have changed, although the default
orientation of "radiological" will be used.

The first of the above commands changes the order of the data that is stored
in the file. The command fslswapdim input -x y z output swaps the order of
the x-axis of the input image to create the output image. It will not change
the orientation information in the header, and so fslorient -getorient will
report the same orientation for both input and output images, although
looking at them in FSLVIEW will clearly show that flipping has occurred.
Note that this way also changes the orientation for Analyze files (and in
previous versions of FSL it was the only tool that could affect left/right
orientation).

The other command that affects orientation is fslorient. This can either
report the current orientation, swap the orientation, or force
"radiological" or "neurological" orientation. This does not change the order
that the data is stored - it only changes the information in the header
which tells programs how to interpret the stored data.

Both methods of changing the orientation only change half of the information
on orientation and so when run separately on a correct and valid nifti file
they will cause the orientation to be inconsistent between data and header.
For instance, if the data is originally correctly stored in "neurological"
order, the correct way to change it to a valid "radiologically" ordered
image (as shown above) is to run both fslorient and fslswapdim on the data.
Alternatively, if the image is know to have the data stored
"neurologically", but the header says it is (incorrectly) in "radiological"
order, then running fslorient -forceneurological will turn it into a valid
"neurologically" ordered image. On the other hand, running fslswapdim input
-x y z output on the same incorrect image will create an output image that
is a valid "radiologically" ordered image.



######
How can one know if the header says 'correctly' or 'incorrectly'?
can't I trust the output info of fslhd and -getorient?
I am afraid that I am big time confused by this.

So if all the template are in Neurological order, what does here mean by
"With the current version of FSL (3.3) we do not recommend storing in
"neurological" convention as not all utilities will work in an intuitive or
"correct" manner with "neurologically" ordered data, especially when mixing
it with "radiologically" ordered data. in FAQ 5"?

I compared with two sets of data, one is converted by mri_convert and the
other is by MRIConverter, which shows me exactly the same header info and so
are the s_form and q_form matrice,but while viewing in fslview, the
activation is the other way around.