Getting back to one of the original reasons I started this, "Does different brass make a difference?"

In ammo.  Short answer: yes.  Does it always matter?  No.

In more depth:
If you're just loading general practice ammo, especially for handguns, long as the cases will fit and cycle properly, use whatever.  If you're going for real accuracy, you have to get picky.

Not always real picky.  Some rifles seem to shoot just about equally well with most brands, but most will have some they do and do not work as well with.  Example:
First rifle I ever really worked on was a 8mm Turkish Mauser, the long infantry rifle(29" barrel).  I did a bunch of mods to it, found a load it liked and then decided to see what difference cartridge cases from different makers might make.  The load, as I recall, was a 150-grain Hornady soft-point over 46.0 grains of IMR4064, ignited by a CCI Large Rifle primer.  Five rounds were loaded with Federal, five with Remington, and five with Winchester cases.

Test day, target at 100 yards.  The Federal set all went into a group right at 1" across, and I was happy.
The Remington set, same size group but centered almost exactly 1" higher.  Still happy.
The Winchester set, group was more than 3" across and both higher and to the right.  Shocked.
That's a fairly dramatic difference, but the kind of thing you can run into.  It's not that Winchester brass is crap, it's good-quality stuff; it's just that this rifle didn't much care for it.

So as little change as 'who made the cases' can make a huge difference, especially at longer ranges.  From what I've read, the serious benchrest types will by cases in lots of 1000(or more) and make sure it all comes from the same manufacturing lot; same for the bullets and primers, and for at least enough powder to fill all those cases.  Trying to keep as many variables as small as possible.  Size all the cases the same, trim to the exact same length, and so forth.  Worth it?  Oh yeah, it helps produce groups like this, and these.

So for general shooting, whatever is handy may work just fine, but for better accuracy, let alone serious accuracy, you'll need to find out which brand cases work best in yours.