Reloading new vs. once fired

The suggestion to load to the same chrono speed is good. You can also fill a new case & a resized case, trimmed to the same length, with a ball or fine grained powder (this is for measuring only!) and compare capacity that way. You can do that with several of each even. If there is a grain or so difference you don't have the same pressure.
If the new brass isn't being sized before firing, then the neck tension idea is also pretty likely.

Is the bolt face square to the bore? You could check the fired brass vs. new for differences that would show that. If that was the situation and the fired base isn't true to the bore, it is like having it long on one side. If that 'long side' is placed randomly in the chamber then it could make a difference. I put an index mark on the headstamp and always shoot with it in the same position when checking accuracy.

Now you got my 2c worth, too!
 
I have been through the same problem. Sub MOA with new brass, over 1MOA with fired brass. Turned out that the chamber was not cut concentric to the bore. After re-barreling, the rifle was fine. Also pays to check that the bolt face is square during re-barreling.

If you check over all of the other potential problems that guys have suggested and still come up with nothing, it just might be that you have the above chamber problem. The new brass is soft and maleable but on the second firing, it can't form to the error within the chamber, the way it did on the first firing. Its not unusual for a rifle with a poorly cut chamber to shoot sub MOA with new brass or factory ammo.
 
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