When Obi-Wan defeats Vader on Mustafar, he leaves Vader alive. Sure, he's missing his legs and has just caught on fire; but when Obi-Wan walks away, Vader is still alive.
I think it's likely that Obi-Wan would have sensed that Vader was still alive until he was a fair distance away from Mustafar, saving Padme.
In addition, we have this line, from Obi-Wan to Vader:
You were the chosen one! It was said that you would destroy the Sith, not join them. You were to bring balance to the force, not leave it in darkness.
So Obi-Wan knew that Anakin was now a Sith. He also seems to hold no hope (at that moment) that Anakin could fulfill the prophecy in the manner in which the Jedi believed he would. It's as if he gave up on Anakin and the prophecy right there.
But he had him! He freaking had him and he let him go! Why not finish him off? All he had to do was walk up and take off his head.
Maybe he didn't want to kill a defenceless man. In that case, why not arrest him to be tried by what was left of the Jedi (Yoda and Obi)? Why just leave him there?