I have shot the 340 weatherby for years. that cartridge is a kicker. I found that using a lead sled for sight in helps. I will develop a flinch with that rifle if I shoot it all the time without the sled for bench shooting. Offhand or field positions are a lot easier for me to handle recoil than from the bench.
I do not like brakes because they are soooo loud. I had one on a 340 and shot an elk.
I did not notice at the time of the shot but it affected my hearing for days probably longer. No more brakes for me.I just will not wear hearing protection when hunting.
In fact I just had a Mark V action rebarreled from 300 wby to 340 (my 4th one) the factory barrel was threaded for a brake. I had my smith install a thread cap instead of the brake.
I have a 300 wsm as well and luckydog is right. the short mag is much easier to carry and shoot accurately. This Mule deer was killed with the 300 wsm. It worked just fine.
Good Luck