Re: .340 weatherby magnum
Both will work fine to 800 meters in my opinion. The difference would be what animals you are considering and what bullets are available to you. The 340 is going to hit with more authority at any range. Since you have the 300 winchester I don't know that it is worth the expense of going to the 340. Others may want to comment. If you were looking to go to 1000 meters or beyond the 338's would take over. But to 800 meters the 300 winchester will work. I have taken animals to beyond 900 meters with the 300 winchester.
Predictions are difficult, especially when they involve the future