Seems the original poster said he had both an 06 and a 7mm rem mag but wants to step up on an elk/moose rifle. Don't have huntable elk here but have hunted moose for a long time and used a .338 win mag for many years with great results, have since stepped down to a 7mm rem mag and don't miss the big gun at all. If I had a 7mm mag I would skip over the .300 right to the ,338 if the recoil was not an issue. A muzzle brake is not a good solution, been there done that have diminished hearing to back that up. One thing to consider is what kind of range are you taking shots at? If your shots are all at 300 yds or less you might also want to consider a .350 rem mag or .35 whelen. Their performance on heavy game far outweigh the paper ballistics.