Greetings Erik7181,
Provided both rifles weigh the same, a .375 H&H with 300 grain bullet has about twice the recoil of a .30-06 with 220 gr. bullet.
Personally, I cannot tell much if any difference in recoil between the 180 gr. .30-06 and 220 gr. .30-06 (factory loaded or equivalent hand loads).
No doubt the 220 grainers recoil more than the 180 ones do.
I am simply too dull to notice the difference.
The .375 H&H is my favorite rifle cartridge for hunting hoofed animals.
It is less destructive on meat and skins than super fast cartridges, such as the various .300 Magnums.
Yet, with a sturdy soft nose bullet it will crumple a charging grizzly or with a solid bullet, it will pass through the massive skull of a large elephant.
Admittedly, I would prefer a larger caliber for elephant hunting and it is over-powered for smaller animals like deer and impala.
Nonetheless, if I was stuck with only one rifle to carry while wandering through the bush (name your continent), it would be a sturdy bolt action, caliber .375 H&H, with a 4x scope in low rings and iron sights as well.
Rifles look unfinished if they don’t have iron sights on them, IMO.
But that is for another thread.
Anyway, you are totally on the right path in seeking a .375 H&H for hunting big game.
Best of luck to you.
Cheerio,
Velo Dog.