I don't have any direct Africa experience, but I doubt it matters at all for the actual hunt. They'll only be firing a literal handful or rounds anyway, and I've certainly never noticed recoil in the field whilst the adrenaline is up.
The main question is around what is comfortable to practice with. Based on most shots being in fairly 'fluid' hunting positions such as standing, sitting or off sticks, again, I doubt it matters. I'm fairly recoil sensitive and more than about 10 shots in a 'fixed' position such as off a bench or prone with a .270 is enough for one session, but I can easily get through 60+ rounds standing during a competition day at the range without any ill effects at all.
I'm not saying you should go for a 375 for the hell of it, but any of the usual suspects of .308, 30-06, .270, 7x57 etc etc will make very little difference for the amount and type of shooting they'll be doing. If you feel the need to buy more powder, then even a 7mm RM or a 300WM would be entirely fine, but really, what's the point?
If you can get a moderator then the recoil and blast is reduced significantly, and here in the UK where they are easy to get, they're practically the norm. I just don't like the nose heavy feel or the unwieldyness enough to bother. A muzzle break is also an option of course, although they can be pretty antisocial to be around.
If recoil really does prove to be a major problem, then a .243 or a 6.5x55 might be worth a try? Can't comment on the performance on African game, but the Swedes are quite happy shooting Moose with the 6.5 and I've seen 350lb Red Deer knocked over with a .243.