I am sure this one will get some juices flowing..
Does the brand of case you use matter? Is one better than the other? How much does case weight consistancy influence where the bullets impact the target?
I personally think that as long as the cases are close in the volume of powder they can hold, then you should be alright for hunting or casual shooting with a good degree of accuracy.
However, when I shoot benchrest matches I favor Lapua Brass. For 2 years I used Remington brass until a friend gave me his Lapua brass with a gun I purchased from him. Being that I bought his rifle for a project, I used the brass in my production gun. (.308) I found the Lapua brass to be more consistant and quite a bit thicker than Remington. (note: the Lapua brass and Remington brass used were fashioned out of 30-06 brass because the neck portion of my production gun chamber measured out at 2.039 instead of the 2.015 SAMMI spec.) The additional case thickness helped with the reduced powder charge and also made the neck portion thicker so they could be turned to a consistant diameter to be used with Wilson Dies at the range.
I did turn the necks on the remington brass, however all I did was knock of the high spots and the neck thickness that resulted was only .014, the Lapua was .026 almost twice the thickness of the remington.
The remington brass developed a 'donut' just below the portion of the neck where the wilson die did not size. The lapua brass did not.
I have since passed the remington brass on to my wife who has starting shooting in our club matches with the gun that was going to be my project gun. She has been doing pretty well, but I would like her to do better. So right now I am working on making 300 brand new Lapua 30-06 cases into .308 so we will have enough for both guns.
For my money I think that for competitive shooting one should use the best materials available if you want to have the best accuracy.