x3 on the Lee Collets and my answer to your question about improving accuracy is yes, the Lee Collet will improve the accuracy components of neck concentricity and consistancy of bullet grip.
I have 2 sets of Redding Competition bushing neck sizers, one in 30-06 and one in 338RUM. I no longer use the bushing die in 30-06 since I got a Lee Collet for it. They don't make a Lee Collet for the 338RUM but after sizing 50 cases the other night with the bushing die, I made my mind up to finally sent a couple of cases to Lee to have them make me a Lee Collet in that caliber. The reason is that out of 50 cases there were 5 of them that had significantly less bullet grip than the other 45. Now these were outside neck turned to fit a tight chamber
and obviously the turner took a little more off on these 5 than the others. I do not have a smaller bushing but it would be a PITA to keep changing the bushing for variances.
I discovered this variance in bullet grip with the bushing dies by gauging with a set of pin gauges
When gauging the ID's of the necks there was some variance. After sizing with any of my Lee Collets there is NO detectable variation in ID. That is because of the way the Lee Collet works. All the variations in neck thickness are pushed to the outside of the neck. With a bushing die all variations in neck thickness are pushed to the inside of the neck unless you leave the expander ball in (and why do that, might as well buy a cheaper FL die).
And would someone please tell me how you can squeeze neck brass onto a non-compressible steel mandrel and "adjust them for neck tension". The only variance should come from differences in work hardening and subsequent variations in springback between cases. I suppose you could only put 10# of weight on the press handle when using the Lee Collet rather than the recommended 25# and that might result in less bullet grip. Don't know how that would help since the Lee Collets put a minimum bullet grip on anyway.