I would make the following suggestion if you embark on these Sigma (or Tamron) telephotos....
Try to see if you can get a loan of a lens and use it in the manner you intend before purchasing. Not just taking it out of the shot and see if you can get a pigeon sitting on an aerial in focus... OH bought one nearly (C variant) 2 years ago for a trip to Costa Rica, and was very comfortable using it outside the shop in Colwyn Bay. Got to our hotel in San Jose, into the garden and we both struggled with it; we couldn't get to the bottom of it but she just did not enjoy using it. Come back from CR and it gets swapped for an XT-3.
I did own a 150-500 PK fit and and thought it was a bit unwieldy. It is the perfect social distancing lens I have to say, people come too close to you at an air show and they feel the lens hood very quickly when I panned.
I have the 200-500 mm Nikkor which in my opinion is a better balanced lens than the 150-600 C. The f6.3 of the 600mm teles does not help my type of photography and I also find f5.6 limiting too.
I cannot comment on the 150-600 S or the Tamron. But please do more than just a cursory focus check at the shop and really test the lens before you buy, you might find one version is more suitable than the other for you,...