Here is a piece I wrote that discusses case neck concentricity.
Mathmans advice regarding neck wall thickness is key here. And I do respect his input and wisdom very much!
Here is why neck thickness is key:
The likelyhood that if the neck walls are a uniform thickness means that the shoulder area and the case body walls beyond the neck/body junction are also uniform (close to the same) thickness. IMO it's the neck/shoulder region of most importance to inducing "runout" during sizing AND bullet seating functions. Visualize the neck & shoulder as a funnel. Now visualize that the "wall" or material thickness of the funnel is thinner on one side. If you apply a tensile load (pull) on the end of the spout of the funnel the side of the funnel at the spout/funnel body that is thinner will yeild while the thicker, therefore stiffer, will resist yeilding.
Likewise, applying a compressive (pushing) load on the end of the spout, the side of the funnel with the thinner walls will yeild whereas the thicker walled side will resist yeild.
What this boils down to is that during the press upstroke the case is forced into the die cavity, brass flows, and assuming die/shell holder alignment and so forth are correct, there will be zero runout of the now sized case. This is true of any sizing die.
For die that has an expander stem, on the downstroke of the press, where the case is drawn down and the die "expander" button engages the now undersize neck I.D. a tensile load is induced upon the case. Say the shoulder/neck walls are of non-uniform thickness, the shoulder/neck junction will yeild a bit while the expander button is pulled through the neck. Runout, or think of it as the neck axis is now "crooked" out of alignment with the case body axis, is the result. If the wall thickness is fairly uniform the tensile load will induce little mis-alignment of the neck/case body axis. Note: it's a real GOOD practice to lube the inside of case neck, being sure to get lube at the shoulder/neck junction.
Also, bushing and Lee collet dies do not typicaly induce runout during sizing. However, when the too large neck is forced into the smaller neck sizing region of the die residual stress may remain in the case neck/shoulder region which will cause the neck to shift a bit out of axial alignment when the case is drawn out of the bushing or collet die. Most affected are case that have a large difference in wall thickness.
Ok, bullet seating. Potential problems here too. Typical interferance (press) fit of bullet/neck is 0.001-0.003". Assume that the bullet axis will be aligned perfectly to the case axis and case neck mouth is square to the case axis. If the shoulder/neck walls are uniform thickness, during the applied compressive load of bullet seating no yeild of the shoulder/neck junction will occur. The now seated bullet should result in a loaded cartridge that has near zero runout.
If shoulder/neck wall thickness is not uniform, yeild may occur, and the cartridge will have "runout", or a non-concentric condition of the bullet axis in relation to the case body axis.
So, result is that some cartridges will have near zero runout, some will have unsuitable runout. Myself, I have noted better accuracy from carts. that have little runout. Whole set of conditions enter that discussion though. Tight chamber-vs-loose chamber, and so on.
JMO though.
Pat