Generally Winchester brass has the thinnest hardest necks so if you have a tight necked gun it may work better, if loose Remington or Federal may be the winner.
If you want to get anal, do a chamber cast and match the brass to it.
In general Norma, Nosler, Lapua and US Natl Match Brass is superior to regular factory stuff.
Unless you're shooting small varmints at long range, almost any factory ammo is accurate enough for big game.
$14.00 a box ammo in a Ruger #1 with a 2-7 Leupold. Would kill anything it is suitable for.