Welcome! First question is, are you talking about serious target shooting with a quality scope, from a bench, or plinking at cans with open sights?
If the former is the case, a 24" fluted bull barrel will offer better accuracy due to higher velocity, less barrel flex, better heat dissipation, and greater stability due to increased weight. Put a 3.5lb lead weight in the buttstock, and you have a rock solid platform on the sand bags.
Concerning the AR10, the -10T in 243Win is a comfortable shooter with longer range than the .223.. The ammo is not any more expensive than quality .308 ammo, and if accuracy is your priority, you wouldn't be shooting cheap surplus rounds anyway. Disclaimer: I am prejudiced towards the .243, as I have one for sale at a reasonable price.
In a nutshell, longer and thicker = better aim and deeper penetration.