What's the best 308 factory load for BC?

I’ve had a great experience with the 168 SMK BTHP (federal match white box) and Hornady 168AMax. Both do well on our Texas deer if you avoid the shoulder joint. Leaves golf ball to baseball size exit wounds depending on the distance and animal.

They rarely if ever exit hogs. Especially if you catch the chest plate. The hogs drop within 50 yards or DRT.
 
I don’t get too hung up on BC as an initial factor or hard data point when starting to look at new bullets. While it is part of the same and greater equation, I concentrate more on stability factor in conjunction with my barrel twist rate from the start. Your 1:10 308 will more than likely not like someone else’s suggestion using a 1:12 twist rate. Play around with this tool and see what might be a good fit for your setup.

 
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