This is clear when you compare his 1941 recording of "You Lucky People, You" to Crosby's performance of the song from the soundtrack to the film Road To Zanzibar. Where Sinatra makes relatively heavy weather of Jimmy Van Heusen's elaborate little melody—pulling away from the beat to make sense of the phrasing—Crosby breezes through the line with insouciant swing, and it makes perfect sense.
Sinatra would learn later to relax on rhythmic lines, but even then his swing remained edgier than Crosby's. "I believed, because of his leisurely manner of working, that if he could do it, I could do it," Sinatra said in the mid-1950s. "The funny thing is that I've never been able to do it. It's just a trick he has, a wonderful relaxed feeling about performing."
Nelson Riddle had a slightly different take on the differences between the rhythms of the two men, "Sinatra digs into a song and tries to get into it," he noted. "Crosby has a calculated nonchalance. He tosses off a tune". This made for terrific rhythmic bounce and cheerful irony, but when contrasted with the vulnerability and poignancy that the volatile Sinatra could achieve with a song, there could be a certain emotional distance in Crosby's work, as there apparently was in his life. Crosby was the original cool singer; Sinatra was the opposite of cool, as a man and as an artist. And Crosby recognized the difference himself: "He creates a mood, which very few people are able to do," Bing once said of Frank. "I don't think I create a mood when I sing."
The two men had different voices, too, and different approaches to them. Crosby rarely ventured from his smooth baritone range to indulge in bravura finishes or extremity of tone. Sinatra not only learnt to make more than Crosby of the expressive "grain" in his voice but would also, at various times in his career, venture to extremes, bringing startling drama to the music, as he did with the high F of "All Or Nothing At All" in 1939 and the low E of "Ol' Man River" in 1963. "Sinatra's voice is more 'live' and vibrant and fraught with shadows and coloring than Crosby's voice," Riddle observed.
Sinatra was always quick to pay tribute to Crosby, saying in the 1940s, "Bing was my first singing idol, and still is." The Old Groaner, meanwhile, acknowledged the rise of the Voice with the oft-quoted quip, "Frank Sinatra is the kind of singer who comes along once in a lifetime. But why did it have to be my lifetime???" He even sent an open letter of advice to the young crooner that was published in Motion Picture: Hollywood Magazine in December 1943. "Keep riding that skyrocket you're on, Frankie! I'm all for you," it said. "Yes, when I heard the whispers about you and me being bitter rivals, I just smiled."
Though entirely different temperamentally and for much of their careers politically, the two singers remained friendly throughout their lives, with Sinatra even singing the old man to his Reprise label in 1962, casting him in the Reprise Musical Repertory Theatre projects and the movie Robin And The 7 Hoods. Their professional encounters, mostly on radio and then TV, were never less than amiable, and their "Well, Did You Evah" duet in the movie High Society was a magical glimpse of the singers' respective performance styles!