I have the 150-600 Sport and 100-400 II. I gave it quite a bit of thought before purchase and continue to evaluate. My comparo thread here:
I put the Sigma ahead (just) in that thread but it's a pure image quality on a static subject comparison.
Bryan Carnathan concluded that 100-400II with 1.4TC is "at least as sharp as" Sigma 150-600C and "similar" to 150-600S.
I cannot comment on the C but agree with the S comparo regarding my lenses.
I can't say what the true focal length of the S is but estimate 580mm and the Canon is around 380mm. When shooting one of these lenses and still needing to crop, every bit of focal length helps so the S has a little advantage there. I suspect 535mm vs 580mm is close to the true focal length of these two combinations.
You mentioned the obvious weight difference, for BIF I would use the Canon due to lighter weight despite the restricted AF points. I have not updated the Sigma's firmware, I'm conservative regarding firmware "upgrades" having plenty of experience with them actually being downgrades (non photography equipment). I find the AF very good on the Sigma regarding accuracy and also speed. Canon is faster but so it should be not being reverse engineered. Accuracy is far more important if speed is acceptable to me and it is for the Sigma.
The IS is superior on the Canon IMHO, for absolute stop gain and to me it's a "it just works" situation. The Sigma can be a bit annoying, has a habit of continually adjusting in one direction in a slow continuous movement then returning to centre in a series of 4 jumps. This is when tripod mounted, on a Benro carbon 4570T with Arca Swiss Z1 Monoball. Not the most solid combo available but pretty good.
I had a problem with tripod ring / foot on my 100-400 II and elected to avoid Canon service and had a private repair shop disassemble and reassemble the lens to allow me to make my own repair. The Sigma foot uses the same bolt pattern and size bolts as the Canon 400 2.8. The foot also has three 1/4 threaded holes to mount a lens plate. It's like a brick house versus a rice paper house. No prizes for guessing which I prefer.
I have used the S in the rain and I trust the Sigma weather resistance more than the Canon. Nothing scientific to back that up, just my personal feeling.
For me the Sigma is worth it but I shoot a lot where an 800 5.6 would barely be long enough. If I had to give up one, it would be the Sigma, due to the size difference. The Sigma, at my estimated 812mm with 1.4TC will still AF, is noticeably inferior to the Canon with a 1.4TC, but noticeably superior to the Canon with 2XTC and that's before up sampling the Canon image that I estimate to be around 760mm which would have no (PD) AF.
The Sigma will be my long solution until I decide to outlay for and find a reasonably priced 500 F4 IS (MK1).
On topic, 100-400II with 1.4TCIII:
Full Image from 7D2:
Discarded just over half the 5472 horizontal pixels for this 2697pixel wide crop: