Sinatra always put me off because I felt that the way he sang his songs (at least in the albums I did hear) felt shallow. I suppose the teenagers of his time might have found his rendition cute, but it never did hit me right. I It was only when I was about to enter university that I started to appreciate his music, and the catalyst was a live album: Sinatra 80th Live in Concert. I used to play it over and over again, and sing with it.
When I finally got internet access, I started searching for mp3's and videos of Sinatra's other albums, and it hit me: I still felt that his early albums were not as good. The clue that led me to understand why was found, of all places, while reading Mario Puzo's The Godfather. One of the characters, Johnny Fontaine, was modeled after Sinatra, and you could divide his career into two phases, before he lost his voice, and after he regained it. And I realized that in the same way there are two phases in Sinatra's work: when he was younger (which I disliked) and when he was older (which I loved). I'll link to two youtube videos so that you can sample how he does the same song, once as a youngster, and the other when he was much older. I think the older Sinatra wins.
Here's the younger Sinatra (1959)