Having experienced this myself many times several things come to mind:
1. Neck thickness difference between both brands of cases. This is especially important in a "tight necked" chamber. Check with a ball mic.
2. Length of fired brass. Carbon sometimes builds fast at the case mouth area. If the Nosler brass is even just a few thousandths longer, the carbon combined with "springback" in the neck area sometimes will "crimp" just the very mouth of the case. After firing a bullet will not want to slide in at because the very front edge of the case mouth is tight. If chamfering the case mouth of a fired case allows the bullet to fit, then take a look at possible carbon.
3. Related to above, if the cases mouths had been previously trimmed and inside/outside chamfered incompletely it may have left a thousandth or two on the inside and/or outside.
Most often carbon in the chamber has been the biggest culprit. Often you can actual see marking/discoloration on the case neck edge. An examination with a bore cam will often show a matching "carbon pattern" in the chamber.
Checking "bullet fit" in fired cases, like the OP did, is always my first check when inspecting before any other reloading process.
Hope you nail down the culprit,
Randy
Randy, great answer, much more useful and tailored to the problem at hand than my 80K foot level answer. Well done.