Some of these guys give advise and they just don't get it.
First of all, a 6 br usually just punches a hole in a chuck at rages of 300 yards or more, they crawl off to an awful death.
If you are going to shoot any caliber on chucks, pick a bullet that is made to expand quickly on flesh, either a ballistic tip, blitz king, or V max....design the cartridge around the bullet, not vise a virsa.
It is real heart breaking to shoot a hole through a chuck just to see him waddle off to die a slow death...maybe you don't care. Most of the target bullets just punch holes through a small animal...they deserve better.
The ranges that you are going to be shooting will dictate a lot of your choices in cartridges. The 75g V Max and should be one of your first choices in the 6/284. The 243 AI will shoot the 75's at 3800 with 1/4" accuracy in a 29" barrel with Win 760. The 6mm AI will shoot the same bullet at over 4000 with extreme accuracy.
In today's world, many guys look at the Highest BC bullet and go for it. The 87g V Max is a good target bullet, but fails in the field at times at 3500 fps on chucks when the ranges got 400+. In your 6/284, the 87g V Max with a heavy load of R#19 @ 3800 will be a winner, and with out a doubt the 75g V Max will T off a chuck 15' or more.
Just forget the 6 BR, I have had a bunch of them. For chucks you need horse power. You don't have 4 shots to get zero'd in on a chuck before he is gone, you get one shot and one shot only. On a rare occasion, you will get a second shot, but that is the exception to the rule. With the trajectory of a 45/70, you just can't deal with taking "sighter" shots with long VLD type of bullets that do not expand at all.
Get a cartridge with some huge balls hanging from it. 6mm AI has the same ballistics of the 6/284 without all the expense of the brass and uses less powder. I shoot the 70's at 4150 from a 26" SS barrel in formed brass from a 6mm AI, shooting 1/4-3/8" groups.
I shot Customs in 6mm Rem on chucks for a long time with a heavy load of IMR 4064 with the Sierra 80g Single shot pistol bullet at 3600 fps, which did a great job.
Good luck!