I noticed a definite improvement in the general accuracy of my .30-06's when I lucked into a few hundred pieces of Lapua brass, compared to the Federal and W-W brass that made up my "general use" stash. That stuff has very consistent case neck thicknesses, easily on par with the LC and FA Match brass that I hoard for "special occasion" use.
I've been working with a Browning single shot .223 that averages 1/2-5/8MOA with Federal brass and Berger bullets. A batch of as yet untried Lapua .223 brass has me hopeful for even better accuracy as its case neck thicknesses are crazy consistent too, better than the Federal stuff which ain't all that bad to begin with.
The devil's in the details.
