Rok, comparing Sheila Jordan and Trane was apples and oranges; the tune originated with the play "The Sound of Music", this is the original "My Favorite Things".
http://www.youtube.com/watch?v=33o32C0ogVM
While Trane's version was killer jazz, it's a long way from the original, and that's why Sheila tops Trane; her version convey's the "essence" of the tune.
In the case of Oscar Brown Jr., you were referring to "Dat Dere", when your post read for "My Favorite Thing". Since he wrote the Lyrics to "Dat Dere" I would hope that he captured the essence of that tune better than anyone else.
Here's Herby Hancock "Maiden Voyage", done by Herby;
http://www.youtube.com/watch?v=hwmRQ0PBtXU
Again, here's "Lenny Andrede";
http://www.youtube.com/watch?v=2B2WicKm0dc
I spent a lot of time cruising in the "Duece", while at the same time going on Herby Hancock's "Maiden Voyage"; Lenny Andrede takes me back to that time; what Tony Bennet said is irrelevant.
Enjoy the music.