The Zambezi River is in Livingstone Zambia or Victoria Falls Zimbabwe. The White Nile is in Jinja Uganda. I did the Zambezi first in the low water season, it was my first real rafting experience. I asked other persons witch one they prefer and they all agree with me.
In short, if you have to choose go for the Zambezi. Both of the rivers have class 5 rapids and I think the Nile have even more of them. In the Nike the rapids are far from each other so you paddle a lot in calm water. In the Zambezi the rapids are closer to each other so it’s provides fast action and low recovering time. The sceneries are also a lot more interesting in the Zambezi, you’re in a gorge between Zambia and Zimbabwe. In the low water season you are very deep inside the gorge and it’s quite impressive. On the other hand, the food after the long day and the quantity of beers available was a lot more interesting in the Nile!