The Sierra bullets will undoubtedly give the best grouping however, the Nosler 140 Partitions do group in the .5 to .6's in both the rifles and maintain that accuracy over a distance.
A friend of mine has a 6.5/06. If he reads this, I expect he will post his loads for you. As I am still waiting for him to post on the Spear Hunting forum , I will take a stab at it.
His main hunting load is 55gr of RL 22, with 140gr Nosler Partitions and non-magnum primers. He gets pretty dang close to 3000fps with this load, and it shoots little bitty dime sized groups. This load is not "too hot" his rifle (no pressure signs whatsoever), but would probably be exceeding safe limits in others. His is based on .270 length brass, so he gets a longer neck, and it also has a very long throat so he can seat those long bullets WAY out.
Canuck