For accuracy, I would opt for the 96 if I wanted a Ruger 44 magnum Repeating rifle. For a single shot, a Henry Single shot would be attractive to me over a Number One Ruger 44 magnum only because of the cost of the rifle.
I've had both and accuracy was pretty even. The 77/44 liked 300 grain XTP's the best. The 96/44 liked Speer 270 grain GD best. I put a Volquartsen sear in the 77/44 and it made a world of difference in the trigger pull. The 96 was stock. I regret selling them both, especially the 96.