Weatherby took the 300 H&H cartridge and blew it out and sharpened the shoulder to make his 300 wby. If you're ever out of 300 wby ammo -- 300 H&H works just fine.
The 300 Win Mag was Winchester's way of shortening up the 300 H&H so it'll work in a shorter action with hopes of trimming the production costs while still delivering the power.
With most things there is a trade off. To gain on one hand you must sometimes give a little with the other. The 300 wby and 300 Win. Mag, as well as many more, all used the 300 H&H case. Actually it goes to the 375 H&H as it came first with the 300 H&H coming 13 yrs later as it's little bros.
The long tapered case fed easily through a rifle, the long neck made it very accurate as it stabilezed the bullet so well. the long tapered case also was very efficient in grs. of powder per velocity. But like i said, it's a trade off. Read your reloding manuals and you'll see. (Speer number 11)
The 300 WBY uses quite a bit of powder to increase velocity by 200 fps. This is hard on barrels and, of course,costs more for powder. But, the 300 WBY starts to pay it's way with heavier bullets. Once you're up to 200 gr bullets the 300 wby leaves the rest behind. And there is a big advantage to shooting 200 gr and 220 gr bullets over a 150 gr or even 180 gr bullets.
So for those long shots, delivering a 200 gr or 220 gr, 30 cal bullet with less drop and ample energy, the 300 Weatherby does pay it's way and that's one reason it's been so popular for so long .
Regards;
Rod