I posed the question as to whether the CCI BR4 primers are suitable for semi-autos like AR-15s, or do they have the same soft cup as the #400s. fxvr5 gave me a link to contact CCI with the question, which I did. Here is their response:
CCI BR4s would be your best choice right behind the 41s as they have a thick cup that helps reduce the possibility of slam fires. With that being said all 3 have been known to work with with the risk being slightly higher for slam fires on the CCI 400s if your firearm is known for leaving a bird peck. Cody B., Technical Service Help. [emphasis added]