Wouldn't mind owning a 300 h&h, but personally, I'd stick with the .338 if I had to make that choice.
Never owned a 300 H&H but have owned a 308 Norma Mag, (2) 375 h&h, and currently own 300 Win Mag and 338 Win Mag. Shot barrel out on 308 rebarreled to 300 WM, gave one 375 to my son and sold the other because I really had no need for them and they had a mortar trajectory compared to the .338.
The .338/210 NP is a hammer on (up to 470#) nilgai cows and (up to 530#) Gemsbok bulls as well as the smaller scimitar horned oryx and much smaller whitetails and is a flat shooter. That has been all I've hunted since 2004 when I shot a 2000# eland bull with 300 gr. Swift A Frame in the 375.
I am hoping to be able to hunt an eland cow (max wt 1200#)this year and, although things not looking good for that hunt, planned to use my pet .338 with either 275 gr. A Frame or the new 265 gr. Nosler ABLR (low drag bonded tipped bullet with an amazing BC of .778! Can push the 338 to 2500 fps w/energy of 3516 @ 100 (compared to 300 gr. 375 @ 2600/4049 ft#) but the low drag bullet catches the 375 @ 150 and passes it @ 200 (338=2282vel/3065 energy compared to 375 @ 1967 vel/2576 energy)
and the 375 drops 10.3" @ 200 while 338 only 4.6!
I feel confident the .338 is up to the task for the eland and God willing plan on giving it a go.
Regards,
hm