I use Redding competition shell holders, the set has five shell holders each .002 *taller than the next. Meaning these shell holders do not push the case into the die as far as a standard shell holder.
*NOTE, these shell holders lower the deck height and thus do not push the case as far into the die. This way the die does not need to be adjusted up and down or moved in the press.
This allows the die to make hard contact with the shell holder and the press cam over with each shell holder. This takes any slop out of the press and more uniform shoulder location after sizing.
The best part about these competition shell holders is you do not touch the die for the amount of shoulder bump, you just change shell holders.
As a example with my 5.56 cases for my AR15 rifles I use a +.004 shell holder to have .003 shoulder bump or set back from their fired length.
If I used the standard RCBS shell holder and the die making hard contact with this shell holder the shoulder would be pushed back .007.
I full length resize all my cases except for mil-surp rifles like the Enfield with oversized military chambers.
Now the main question "Do die brands matter?"
I have seven .223/5.56 dies of different manufacture and type, bushing dies, neck dies, full length dies and collet dies.
My favorite is the Forster full length benchrest die set, it has a high mounted floating expander. The neck of the case is still held in the neck of the die when the expander enters the case neck. Meaning the expander can not pull the case neck off center and induce neck runout.
Also if you have a standard off the shelf factory rifle, bushing dies can induce neck runout when they reduce the neck diameter .005 or more. Meaning these bushing dies work best with tight neck chambers and neck turned brass.
We live in a plus and minus manufacturing world and dies and chambers vary in length and diameter. Example, I have a standard FL Lee die that will push the case shoulder back .009 and reduce the case diameter smaller than a small base die does.
At the massreloading.com website they show that dies can vary .005 in neck diameter between die manufactures.
Are Your Sizing Dies Overworking Your Rifle Brass?
http://www.massreloading.com/dies_overworking_brass.html
Bottom line, in my opinion the average reloader would be better off full length resizing using Forster benchrest dies. This is because they produce the least amount of neck runout and the most concentric cases.
The Forster high mounted floating expander and spindle assemblies work so well I put them on all my RCBS dies to reduce neck runout.
Most neck sizing dies do not fully support the case body during sizing and can induce neck runout. And at the Whidden custom die website they tell you that non-bushing full length dies sizing dies produce the most concentric cases.