Both calibers you mention are fine.  Plains game varies a lot more in size than people realize.  The trend now is for hunters to bring set ups with 3 and even 4 interchangeable caliber setups.  Its nice to only register, check and travel with one set up.  Your outfitter has to indicate how much is Safari Style and how much is true spot/stalk.

African plains game can vary from 1700 lb Giraffes and Eland down to 20 lb pigmy antelope.  Most first time safari hunts are for animals like Kudu, Gemsbok, Impala, Blesbok, and Warthog.  You want to bring a rifle that you are familiar with, you are comfortable shooting, and is adequate for the largest animal that you will be hunting.

Although many animals prefer certain habitats to types of vegetation to live in, many animals are shot as the opportunity arises.  For example, you may be stalking a 600 lb Kudu bull when you jump a 30 lb Duiker.  You have to make a quick shot, and you probably won't have time to switch rifles (or barrels ?), even if you have someone else carrying them with you.

Many consider the African Kudu equivalent to our Elk, so a good Elk cartridge would be a good Kudu cartridge.  The .30-06 and 7 mm Rem mag are good Elk cartridges, and are also good cartridges for African plains game animals with the right bullets and with the right bullet placement.  160 gr Accubonds worked well for me on one SA plains game hunt, 180 gr Partitions worked well for me on a pile of Colorado and Montana Elk.

Remember that in most of Africa, if you shoot and draw blood, you pay for the animal whither you kill the animal or not.  On most African hunts, you pay a daily fee then a trophy fee only on the animals that you shoot.  Some of those trophy fees are into the thousands of dollars.  You are also limited in your time there.  Do you want to spend your time hunting or do you want to spend your time trying to find an animal that you wounded with a poorly placed shot or that was hit with an inadequate caliber or bullet?

On my last trip to South Africa, I wanted to keep things simple so I only took one rifle, my .375 RUM.  It worked great on everything from Eland and Kudu down to Steenbok and a Jackal, although there was considerable damage to the smaller critters.  I borrowed a .308 Win with military FMJ bullets to minimize the damage on my Grysbok.

Dear hunter25,

The minimum caliber permitted is a .270. The 30-06 is capable of taking most of the plains game available. The 30-06 in my mind is the absolute minimum to be used on Blue Wildebeest, the BWB is not called the poor man's Buffalo for nothing. I did not include Class 1 here as the Min Caliber for the following is, .22 Hornet, .223, .243;  Suni, Dik-Dik, Blue Duiker, Rabbits, Game birds, Gazelle, Minor antelope, Reedbuck, Lesser Kudu. Your 30-06 will suffice for these.

Class 2 – Large Game
Major antelope, Zebra, Greater Kudu, Sable, Roan, Waterbuck, Wildebeest, Hartebeest, Lion

25-06, .270, 7mm RM, .308 Win, 30-06, 300 WM, .303 Brit, 9,3 x 62

2500 ft. pound of energy

Class 3 – Dangerous thick skinned game
Big game, Elephant, Rhino, Buffalo, Hippopotamus, Giraffe

.375 H&H, 416 Rigby, 458 WM, 505 Gibbs

4000 ft. pound of energy

Trust the information is useful.