These are two of the most visually stunning, remote, and game rich places on the Planet. To combine the two areas is preferred by most during the dry season; in Chobe the elephants are amazing, plus lots of other game, and the bush is not so dense so viewing is outstanding. In the “Green Season”, November – March, the animals disperse because water is plentiful south and the wooded area gets pretty dense, but you still have the wide rivers for birding.
If you are traveling during the African summer, I recommend visiting one of the Sabi Sands camps in South Africa, followed by Moremi. If you are traveling in the African winter months (May – October), I would also recommend Sabi Sands, but combined with a split between Moremi and Chobe for phase two; this would give you a nice mix of ecosystems, tons of wildlife, a nice mix of safari camps and guides, and basically just the opportunity to see, do and experience many different sensory pleasure .
Take a look at related travel and holiday packages in other countries.