Did you consider the .270 win or .270 wsm. If she is comfortable shooting it, the .270 has enough horsepower for elk sized game. I would prefer shooting a lighter cartrige more accuratly than a bigger bullet with significant recoil....
In rifles of the same weight,the 308win will produce less recoil shooting a 165gr bullet than a 270win shooting a 150gr bullet.The 270wsm will produce noticeably more recoil than either of the other two.