I have noticed that the Remington 61/2 primers seem to be smaller in diameter than the other brands. They seat very softly into the small rifle cases. I have measured them and have found them to be smaller than Winchester and CCI primers in diameter. Federals are just a little larger than CCI or Winchester.
Bottom line is if you have tight primer pockets use the Remingtons. If the primer pockets are loose use Federal.
I mostly use Winchesters in my .223 loads and have had good results.
The Remingtion Benchrest primers that I had did not seem to be smaller
but I had purchased the 61/2 primers and was disappointed as they seem to be a loose fit in the .223, 25-20 and the .30 carbine.
They still work great but I prefer a tighter fit when seating the primer.
Of course different lots may vary but I would skip the current batch of Remingtons in the .223.
If shooting a AR the Remington primers have been know to blow out and jam the rifle. Seem like I got best service from winchester primers with a load of 748 for match ammo.
From what I've read Remington recommends their 7 1/2 primers for .223 ammo especially when used in a semi-auto. I don't use Remington primers so I can't tell you first hand. I prefer CCI or Winchester primers.