I would say the 308 would be at the head of the pack by a fair margin on deer size game. I would place the 6mm BR and the 6.8 as pretty close in performance with the slight edge going to the BR in my opinion.
I do not feel the 6.8 and 6mm BR are big game rounds for use outside 400 yards on the BR and 300 on the 6.8.
Just my opinion. If your hunting smaller game such as coyote size game or fox size game, I would pic the 6mm BR as my top choice, 308 second and 6.8 third with the last two being very similiar.
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