It's wet season for both Botswana and South Africa at that time. It won't necessarily rain all the time but the grasses are longer and water abundant for the game so they animals can be harder to see and the spread out. January isn't ideal for a safari but scenic and cheaper.

The Okavango Delta area is huge and although Abu Camp is closed there are other camps open at that time of year. If it were me I'd go to Botswana.