As noted in my post #19, for me it's primarily a matter of practicality rather than accuracy - will the reloaded ammo chamber & function consistently, or not?
Fact: some .38 Super cases can handle my long 160 gr cast bullets without bulging, others cannot (because the case wall thickness increases at a higher rate towards the case head, and the walls are thick enough at the bullet base to bulge when a 160 gr bullet is fully seated). Fact: sorting by brand is NOT sufficient; some Winchester cases have thin walls and do not bulge when loaded with the 160s, others have thicker walls and bulge enough to interfere with chambering. (FWIW, it's not just Winchester .38 Super cases - Winchester .40 S&W cases have extreme variations also.) And sorting by weight can be quicker than checking the wall thickness of each case with calipers, at least in my experience.
So, if you load traditional (short) 115/124/130 gr bullets, you're probably ok if you just sort by headstamp. If you load longer/heavier bullets, however, and sort only by headstamp, you'll end up with an inconsistent mix of bulged/unbulged reloads, with unpredictable reliability & performance.
As noted in my post #17, I also weigh cases when I'm comparing loads/different propellants. That can help reduce variables and identify potential problems (like bulged cases) with particular combinations of components, as well as increase my confidence level if one particular propellant looks more accurate than others. For example, when I was looking at .38 Special +P 110 gr JHP loads, I checked my references, and found some safe loads for 4-6 different propellants I had on the shelf. Turned out that I had markedly better results (in my firearm) using IMR- 4227 than the other propellants I tested, and I'm confident it wasn't due to some random mix of bullets/cases/primers for the 50 test rounds I loaded for each propellant. Is my 4227 load capable of match-level accuracy? Probably not, but that's NOT what I was looking for - I was just trying to find the best combination available to me, using components I already had, that would suit my needs and maximize consistency/reliability/safety/performance.
As always, IMHO, FWIW, YMMV, etc., etc.