6.5 Grendel if you do not reload. 243 LBC/6mmAR if you do reload (6mm Grendel variants).
The Valkyrie is only marginally better than a 223/5.56. What a 223/5.56 can do at 1150 when port fed, the Valkyrie can do at 1300 from the mag. It’s not as much of a step up as the Grendels.
These cartridges offer massive advantages at 1,000 yards over the 5.56/223. It’s absolutely true that a 223/5.56 can easily play at 600 without much issue, but things become exceptionally challenging around 800, and almost laughable at 1100 compared to the 6.5 Grendel or 6mm versions. It goes without saying, the extra ~20% case capacity for the Grendel over the 223/5.56 is a big advantage in terms of what can be done with these rounds, and the extra bullet weight isn’t trivial in terms of fighting wind and impact indication. Paper games at 1,000 yards is tough with any cartridge unless you have target cams, but even with steel targets, you’re talking about a LOT more vulnerability to wind on the little 22cal bullets compared to the 6 and 6.5mm pills. None of the AR cartridges will hit a big steel target hard enough to really rock the boat like a standard short action cartridge, but the small 22cal pills, especially anything mag fed, won’t give indication at range nearly as much as the 6mm or 6.5 Grendel. A 77 SMK or 73 ELD in a 7 twist 24” barrel will get you to 1,000, but you’ll have a lot more headaches than with a Grendel.
It’s also true to say a 6.5 Creedmoor is a better choice for long range shooting than a Grendel, but you’re starting the “a little more is a little better” game. The Grendel is cozy at 1200 yards, and will get there with 30% less powder, two pounds less rifle, and about 2/3 as much recoil. Buying or building a long range AR-15 will also typically cost $500 Less than building a similarly kitted AR-10. If a guy is “serious” about long range shooting, defining that as 1,000 yards, then the 6.5 creed isn’t the best choice either, nor is a gas gun, whether AR-15 or AR-10 sized, so this discussion is really around defining what brings you joy. With the objective of casually plinking at 1,000 yards with an AR, then I would pick an AR-15 over a 10, and would use a 6mm or 6.5 Grendel to do it (and I actually do exactly this). If 1760 is on your horizon, then an AR-10 in 6 or 6.5 Creedmoor might make sense. But for 1200 yard and shorter plinking, the extra horsepower of the Creedmoor case isn’t worth the extra baggage.
So yeah, 6 or 6.5 Grendel, depending upon whether you reload or not.