I bought the 100-400mm MKII as its compact and stellar IQ. With todays cameras 5.6 is great unless you want less DOF which is nice but with birds you usually want more to make sure everything is in focus.
Took it traveling around the world with a 5DMKIII and a 7DMKII. I also took a 1.4x and used it 3-4 times as I didn't need it. The 7DMKII gets a bad rep but mine is a great copy and my 5DMKIII got a lot less use when it came to wildlife which was my primary reason for having the lens.
Granted on my 7DMKII its 640mm and once you get to that point atmospheric issues come into play especially in hot places like Africa.
I absolutely loved it. I like you would love a 500-600 but they are cumbersome and I've always found fixed focal lengths to be inconvenient especially at that size.
On Safari I would have hated using it, I was forever moving around in the car and there is usually 4-5 people it just wouldn't have been practical. You also get a lot close than you would think. Also I was back packing, carrying the weight for the 100,000 miles would have been a pain. My bag already weighed about 14kg with camera gear, with some supplies 16+ then I had a larger bag with all my clothes etc which was 20kg so a lot to carry around. Granted the 20kg bag wasn't with me all the time and was left in trucks or tents or truck etc but when your on the move you have to be able to carry both between transport and rooms, catching trains etc.
The 100-400 is so versatile its fantastic IMO. But with birds you always want more so the 5DSR might be a good option or if you want to spend less the 7DMKII really is a fantastic camera. I shot it up to 6400ISO and had no issue at all.
For example
I know its not a bird, gorilla in Biwindi NP Uganda but its tack sharp has a little noise but didn't struggle at all. Unfortunately I haven't got any birds that I photographed on hand but there were many thousands along the way.
My first travels through South America I took the 70-300 with my 5DMKIII and it was way too short but had a very happy back. Took it to the amazon and always felt like I needed more. Will return with something a crop + 100-400mm
Don't get me wrong if I had the choice I would take a big lens but you have to carry it and in tropical rainforest heat its so hard. I trekked 6 hours in 45+ deg humid rainforest through hard terrain to see the Gorillas and I struggled with the 5DMKIII + 24-105 and the 7DMKII and 100-400 on my back with water food etc but it wasn't a trail we had to make or way through with Machetes so probably not the average trip but thats the sort of thing you have to do to get to these incredible creatures.
You can always hire a porter but I find it a little disrespectful.