With your 6mm Remington you are covered as long as they are accurate and safe, that's my goal anyway. Accuracy is always better than velocity as many have said. That's why we are here.
What is accuracy? Is it the best group? Is it 1 shot hitting closest to the point of aim and a great group? Is it 1 shot hitting at point of aim but 4 more producing a ho-hum group.
I shoot at ranges to work loads, I average groups particularly under adverse conditions, hot and cold as I can get, calm and windy. I practice field positions, acquiring and firing as fast as possible, within 5 seconds is my goal.
My 2 varmint rifles a 223 in a Howa 1500 varmint kit rifle and a 6MM Remington in a 700 Remington BDL varmint. Both rifles will chime in on average at 1 1/16" groups at 300 yards.
Is that the best groups that these rifles can do? No! I can get both rifles down to 1" at 300 yards, the 223 only in semi-rare light wind conditions.
However the velocities in both rifles that produce the best groups produce unacceptable trajectories and wind resistance for field work and the best groups on average are only 1/16" better. In respect to the 2 1/2" target area of a chuck or a crow the question is how relevant is that 1/16"?
The groups that I use produce with the higher velocity loads produce the ability to place a round on target in a wider set of variables. Especially the 223, a extremely faster 40 grain, (3,900 FPS) handles wind and shoots much flatter out to 350 yards better than heavier weight projectiles in my rifle.
Similar can be said about my 6MM Remington but the range increases to 500+ yards. I shoot 3,900 FPS with a 75 grain VMAX, within the effective range heavier projectiles make hits harder in the field.
Same process can be handled for medium game, pig, deer, elk, except the target area is 4". I would argue that velocities value need be weighed even heavier than an additional 1/16" group improvement as in this vcase energy/knock down value on target is far more critical with larger game.