In my country informal requirement for hunting rifle is to make a group of maximum 4-5 cm at some distance. Assumed that target is most common European big game (a roe buck), and delivering a lethal shoulder shot.
The size of group will also determine useful range of a rifle in hunting for individual hunter and his (scoped) rifle.
Two inch group is not much of a accuracy requirement, if we are speaking of at least 100 meters ranges. As per our law - maximum range in big game hunting is 150 meters, in order to prevent wounding of animal
Reading it other way - extreme accuracy is not expected from a hunting high power rifle.
On the other hand, long range target shooting equipment will need to have sub MOA accuracy.
The competition rules say that you will fire 10 rounds in 10 minutes at target at given ranges (usually 300 and 600 meters). So, the competitors will surely want their barrels not to heat up too much, as thermal dilatation of barrel may change ballistics of rifle with bad effect on target. That's another characteristic required. However, we are still talking about sport.
In professional sniper rifle, I guess - one shot - one kill rule applies, so barrel heating is not an issue in repetitive shots, but sub MOA accuracy should apply, especially for long range shooting.
In conclusion, I would say - sub MOA accuracy for longe range target shooting and sniping. Plus MOA accuracy for hunting.
Having said that, this will define another difference: high performance rifles will cost higher with their expensive barrels, then medium class rifles for hunting with hammered barrels of cheaper production.