I always thought Sonny did not sit in his father's chair because it was "the Don's chair" and Vito was still alive, and it was out of some kind of respect. That said, DC you could be right for several reasons.

No question Sonny doubted himself. Again I refer to the flashback scene in GFII. When Sonny is introducing everyone to Carlo, he insults Mike by introducing him as the "droopy" kid, and saying "We call him Joe College." We see it again when Sonny mocks Mike in the "Badda-bing all over your Ivy league suit" scene. We also see it in his relationship with Tom when he says "Pop had Genco, look what I got..." and then IMMEDIATELY he apologizes to Tom (something Michael would never do even if he was wrong to say it). Sonny was very much the stereotype of the son of a famous and powerful man. You could also see it in the scene where they were all sitting around eating chinese take out food (yes I know some say it was Italian)while they were waiting to learn where the Sollozzo meeting would take place. At one point Sonny says maybe Mike shoud just shoot them when they picked him up, and Tom had to shout him down. Then when Sonny learns where they are going he is a little too smug about it, which was a great piece of acting by James Caan.

It was thrust upon him early, and he always knew he had big shoes to fill, and no question he knew he could not fill them.

Footnote - In the Havana scene with Mike and Fredo both of them also touch on this subject. Fredo says he wishes he had married someone like Kay and "for once in my life be more like pop." To which Michael answers "Its not easy being a son."