Absolutely NOT! About the only similarities they have are the same bullet and case diameters. The 6mm AI is the full-length 6mm Remington with the case walls blown out to maximize capacity - improved velocity was the goal. The 6mm BR is a shortened .308 case designed to emulate the 6mm PPC's accuracy performance. While it is a very good cartridge in its own right, its design goal was different than the 6mm AI's. I had a 6mmBR with a slow twist that worked great as a varmint rifle with 55-grain Nosler BTips. It gave slightly better downrange performance than a .22-250 with 'better' accuracy and terminal performance.
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