It all depends. If this is the one and only safari you ever intend to go on, then the 30-06 and such is just peachy.

But if this is just the start, a .375 H&H is better. The plains game hunt turns into practice for the big stuff.

And if you are in dangerous game country, you should be carrying a dangerous game rifle, of which the .375 is the minimum, regardless of any regulations.