Pippa:
You are a brave lady. I had thought of renting a vehicle in Mombasa and driving to Tsavo but the Nairobi-Mombasa road is so bad that I wouldn't now dream of it.
That, plus (Kenya at least) and perhaps all of Africa don't have many road signs. I'd still be driving around the round abouts in Mombasa trying to get out
You'd also have to know how to drive in all terrain. A Kenyan family went on a game drive in August. The son, who stayed behind in camp, came to dinner at night and failed to tell anyone that his family had never returned. At 7 a.m. the next morning he decided to tell the manager. They sent out all the safari drivers out looking for them and found them and their overturned vehicle. They had apparently driven into the sandy shoulder part of the road, flipped the vehicle over and had injuries. They had stayed in the overturned vehicle all night hearing the lions roar around them until help arrived. All had to be air lifted to a Mombasa hospital.
Thus though I've been driving for over 50 years, I don't know if I'd ever have the nerve to drive around Kenya by myself (without a weapon).
The explanation I've had put to me is that for many parks/reserves Landcruisers are fine. However for Tsavo where the mud in rainy season can be really bad, only the Land Rover will do. I personally prefer a newer Landcruiser than an older Land Rover. They are far more comfortable. But I'm told the tourists like the "romance" of the older Land Rovers Don't quite buy that one though.