I have a .240 Wby built on a Winchester action with a medium sporter weight barrel. I built it almost 30 years ago and have used the .240 Wby on pigs, goats and fallow deer with great success. It hits hard for a 6mm caliber on the size game mentioned, if you place your shots well. In the early days I used the 95gr & 100gr partitions. They were and still are a good bullet in the .240 Wby. A mate of mine took a number of red deer with his Mk5 lightweight in .240 Wby at ranges under 200yds with the Partitions. I don't think its a red deer cartridge but certainly did the job at the time.
I used the 85gr Barnes TSX for a number of years. They zip through everything I every shot with them. That's not a bad thing. Just an observation. Now I am using the Swift 90gr Scirocco II because my local gun shop had a couple of box's and I felt like a change. The Scirocco's seem to kill faster and drop fallow deer and pigs faster than the Barnes did.