Collimation - star test or Cheshire?

Checking the collimation on my MN-56, there is a slight
disagreement between the two techniques. When I align using
the center mark and a Cheshire, the out of focus star test
is not quite concentric, and when I get the center-of-the field rings concentric, the Cheshire results are a bit off.
I know if the center mark is not accurate or if the optical
center of the mirror does not coincide with the physical
center, then that will throw the Cheshire off, so is the
out-of-focus star test ultimately the most accurate method
for checking collimation?

I've had exactly the same problem with my MN 56. Once the star test is good, move the focuser so that the Cheshire dot is centered where it should be (Do this without moving the primary or the secondary, I shimmed one side of my focuser for the best result). Mike Palmerti told me that is an inherent problem with the Rusiian focuser, and it is.