Once you reach a certain level of greatness, in any art, I think it becomes subjective. IMO, Nat King Cole has a great timbre, but he sings everything pretty straight. I tell you one thing though, he was one of the best bebop piano players ever- most who know his work in both areas, believe he was by far a better piano player than a singer. That said, I love Nat King Cole, if for no other reason than his voice quality and his economical choices.
I'm starting to feel like the only Sinatra fan on this board- which is strange considering he's probably the most popular of his genre. However, Frank did not have the best voice, he was not the best improvisor. He did not sing the amount of jazz that I would have preferred, and almost exclusively sang with a big band when the few times he worked or recorded with a combo, he did it well-- though he didn't have the head voice of say a Tony Bennett which lent more to that kind of intimacy. Another guy who I don't think has been mentioned on this thread is Mel Torme, who was a very creative singer. But, Frank did all of these things well enough, and the one thing I think he had over all others of his genre, was taste. Plus, and this is very important, Frank was a big enough moneymaker that he could call his own shots in the studio. Since he left Columbia and especially when he started his own label in Reprise, he had control over what songs he sang and how they were arranged. A lot of these other guys would have potentially been just as big as Frank if they'd had his juice. Few did.