I had a 100-400mm until recently and now have the 70-300mm, The 100-400mm is fabulous, and would be great on a safari or very much dedicated wildlife trips or similar. When I bought it, it was specifically to take to the Le Mans 24 hour race. For that, it was excellent but... it's very big and heavy and it meant that I just didn't take it unless I knew I was going to be shooting something that justified it which was almost never for my normal type of photography. The 70-300mm is tiny in comparison and IQ appears to be on a par but of course you lose 100mm of reach (300mm is still quite a lot of reach on an APSC camera though). For me, it makes far more sense, and I can take it anywhere but I have to admit, if I were going on a safari, I might have tried to get hold of a 100-400mm temporarily or even a Tamron 500mm or Fuji 600mm zoom which are even bigger! Worth mentioning that you can use the 1.4x with the 70-300mm as well and it works okay in my experience.
I haven't used the Sigma 16-300mm. but I did give the Tamron 18-300mm a try which is a similar proposition. Really impressive in many ways as it delivered quite good IQ throughout the zoom range which is perhaps not expected with such a huge zoom range. AF wasn't that impressive though. I used it for a weekend in the Scottish hills and it was nice not having to change lenses in that environment but again, for a lens that you might wish to carry all day, it's quite big. I would assume the sigma is slightly bigger still. Interesting lenses but quite a compromise in my opinion.