We all simply prefer what we prefer. Compared to Sinatra, I thought Dino had a weak voice. You don't hear him really push out the sound the way Sinatra does on his more epic performances. Also, I always thought Dino had a lazy, laid back approach that does not work for some songs. Dean gave a few really good acting performances (particularly in Rio Bravo), but most of his acting IMO is also of the lazy phoning it in variety. I don't really mean that as a criticism of Dino. He was fairly up front about how he performed. When he did his long-running TV show, he was practically forced to do it. He only did on the condition that he always got to wear a tux, and that he never had to rehearse. For a relaxed, lazy sound (sometimes that is what is called for), Dino is unbeatable.
That clip of Sinatra singing "It Was a Very Good Year" isn't even Sinatra in his prime. His vocal peak was probably 1958, but he still made some great recordings, even though his vocal instrument had lost a little.
While I, too, preferred Dean Martin over Frank Sinatra, neither of them held a candle to the best singer and performer in the Rat Pack ...
Sammy Davis, Jr.