I have done both. They both have some upsides and downsides. I'll try to be brief.
QA Upsides
They are excellent with guns. A bit of a paperwork process, but they don't let you get on the plane if your guns aren't on also. They check this at the gate. I know this as I have been momentarily paused at the gate until they confirmed my rifle case was on board.
The QA flight to JNB from Doha can scheduled to arrive as early as 4am and the next being at about 9am or so. I like arriving in Africa in the morning and forcing myself to stay awake that first day. This gets me on Africa time quicker I find.
QA folks are generally much more customer service focused than Delta.
QA Downsides
The extra flight does take time. On the way to Africa I'm not bothered by it. On Delta, you'll likely spend an evening in JNB whereas with QA you won't. So in the end the actual travel time is about the same. But on the way back home, those extra hours in an airplane catch up to you, more so as you get older
They make you weigh your carry on and restrict that to 7kg and their rules on their website are a bit fuzzy. You'd be surprised how quickly you put 7kg of stuff in carry on.
Delta Upsides
No extra paperwork for your weapons. Just go to check-in and the subsequent TSA routine and your off.
It is quite easy, just get yourself to Atlanta which is easy to do.
Shortest trip to JNB in regards to air time.
Delta Downsides
Delta staff treat your more like livestock than people in general. There's always the exception but the general feel is not as nice as when flying on QA.
Delta's on time schedule I believe is not as good as QA's. Ask
@Royal27, he's been up in the air twice out of Atlanta and got turned back......twice!
The arrival time in JNB is what I dislike most about Delta. Late in the evening, you need to make it to a lodge. By the time you get to the lodge, checked in and maybe a bite to eat, it's about 11pm when your head hits the pillow. In about 3 hours give or take, your head will pop right up and be ready to go for the day. And there you will lie just praying to fall back asleep as you watch the clock move. Every time I do that flight, that is the result.
So, pick your poison is the best I can say.