Timothy, If you will be hunting deer mainly and elk once in awhile, I would go with the 300 version with a bullet such as the 200 gr Accubond for longer range stuff if you did not want to use a match bullet. For elk I would recommend the 200 gr Accubond simply from an on game performance stand point. That said, it never does any harm to be over gunned if you can shoot the things accurately. A good reason for considering the 300 is with the 340 you really don't have a lot of bullets to choose from like a 30 cal. To be honest, either are fully capable of covering all the hunting you want to do. Landing the bullet in the right location is a far more important factor.