Like Bob says, the ease of finding 340 Wby brass/ammo is much, much easier. 340 Wby cases can be readily made from 375 H&H brass, though I feel 8 Mag brass or 300 Wby brass is easier to use. One pass through the sizer die makes perfect 340 cases whereas 375 H&H cases need to be incrementally sized down or the case may collapse.
Yup. CW is right.
Just used the 375H&H case to illustrate it can be done,but the others may be easier. My buddy used to form from 375H&h stuff,which is why I mentioned it. The 340 is based on the H&H case....I think it's just the 300 Weatherby necked up.