Truth be told, Dooku held real respect for Kenobi because of the latter being the true elegant Jedi and considered him one of the last of the real Jedi. He even felt sad about the perspective of killing him in RotS novelization. Not much of course, but for a sadistic freak Dooku was, that's still something to behold.
And as well, while ironically, Obi-Wan also acted gentlemanly towards Dooku. The dynamic between the two resembles Sherlock&Moriarty from some works, lel. The gentlemen rivalry with no quarter given either way.