Here are a couple of good, balanced articles on the subject.

Both give the edge to the ‘06 with heavier bullets.

Outdoor Life

American Hunter

Is it enough of an edge to influence a reasonable man’s choice of caliber for an African safari rifle?

It’s enough of an edge to make me prefer the ‘06 when using 180 gr. and heavier bullets.

And for African big game in the 400+ lbs. range, I do want the heavier bullets.

YMMV, of course.

Mike,
Thanks for the articles.
All in all, both will do the job if i do mine....
I like 165gr in both along with 150 gr in the .308.

They both shoot well.

I've used the 308 a bit in Africa but mostly in the US,,Ive used the 7x57 extensively in both the US and Africa, they are equal and as effective as the 06 and its get on big game..bullet placement is as important with them as it is with any caliber..

I brought my 308 out of Africa and used it in North America. Does that count?