Namibia +/- Botswana advice - both or just one?

Hi all, I'm headed to Namibia in June next year on a 11 day group tour covering the highlights including 2 nights in Etosha. We're considering flying to Botswana after the tour to spend 2-3 nights at a safari there independently. My questions to those who've been to both countries: Would be worth it to make the trip? As in, would our experience on a safari there be significantly different to what we would get in Etosha to justify the time/cost of getting there. We would need to fly from Windhoek to Botswana via Johannesburg ($$) as there are no direct flights, and then back to Johannesburg to get on an flight to Europe (where we will be continuing our holiday, therefore, time in Botswana = less time elsewhere). If the answer to the above question is "yes", then would you recommend Chobe vs Okavango vs somewhere else? I'm thinking about places that would offer a unique experience compared to Namibia as well as wildlife sightings. Thanks in advance!