I see this is your first post, so not sure if photography is a big hobby for you, or you are asking for your trip.
I would answer your question like this, it depends on what part of the world you are in. If I were going it would be a rare trip for me. I have looked in to a few safari and they would cost the wife and I in excess of $20k. It would probably be a life time trip for us as there are other similar trips we want to take to.
That said I would rent the 300mm f/2.8 II with both extenders. Since it is a one time trip that cost quit a bit, renting a nice lens is small in comparison. Plus photography is my passion.
If it isn't a life time trip, or if your just looking for a good lens I would go with the 100-400mm. I would prefer the better IQ at the long end.
I would also consider the 70-300mm L, it is more compact however you are not supposed to use an extender on it.
If you have not been on safari and you do not know what the practicalities are, you should not give advice. Sorry to be blunt, but you could spoil someone's safari. I have the 300mm f/2.8 II with both extenders and I certainly would not take that as my sole lens system. For much of the time you would not have the flexibility to take closer subjects. You MUST take a zoom on safari. Next time I go I will take my 100-400mm and the 300mm + 2xTC with two bodies. That set up would give me the flexibility of zoom, and a wide aperture f/2.8 for low light, and 600mm for birds and distant wild life. If I am restricted to one body and one zoom, it will be a toss up between my 100-400mm and my 70-200mm f/4 plus extenders. If I had the 70-200 f/2.8 + 2xTC, I would take that for use at dawn and dusk at f/2.8 and a lens not far off the 100-400mm with the extender.
I didn't claim to have gone, only that if going on a trip such as this I wouldn't skimp on the gear. For what it cost to go I think that is sound advice. You can take your arrogance elsewhere.
I have done the research through several outfitters. While you may have experience a certain type of safari it doesn't mean your have experience in all. The best source for information would be your guide. The guides I researched were geared for photographers and guided by photographers. They were partially by vehicle but portions of the trip were backpack and backcountry. The recommendations were for a lens like the 300mm with a second body and shorter zoom for the close up ad wide angle shots. Carry both with you at once, after all you are a photographer right?
Now I do not care if I am going to Africa or walking down the street to take pictures of rabbits at the park, there is no way I am using the 100-400mm over the 300mm f/2.8L just because the 100-400mm is a zoom. I will give up the few pictures I miss because they are to close, anything on the long end I can crop and get better results. I seldom take memories, the hobby for me is the photograph itself and the 300mm will do the job.
Never been but this is the list I would take. If this list spoils his safari then he isn't much of a photographer.
Three bodies, 5D III, 1D IV and the T4i for the wife. I would take 4 lenses the 300mm, 70-200mm f/2.8L II, 35mm f/1.4 and 24mm f/1.4. I would take the wife and we would share this load. Monopod and a tripod as well, would tailor the tripod to the trip. Backpacks for both of us to share the load.
So my primary advice is don't skimp if photography is your passion. If you are collecting memories the 100-400mm is a fine lens for doing that and it will make almost all non-photographers happy no matter where you go. In fact it will make many photographers very happy.