They have more of a personal heated rivalry and it has been that way since the early 90's! Sonny and Jax have competed intensley over women (Brenda, Carly etc) and Sonny views Jax as a threat to Carly, he's the only man that he thinks can take Carly away from. Sonny also knows he can't kill Jax, because of Josslyn and to a lesser extent Carly, which in turn makes Sonny feel powerless.
With Julian its mob business, and nothing personal! Prior to 2017, Julian has been gunning for Sonny's terriotiory and in turn trying to kill Sonny as well, and Sonny has tried to kill Julian in turn, to keep him from overtaking Sonny's business. To Sonny, its just "mob business", and really it hasn't been personal, however, I think that will change once Sonny learns that his grandson is alive and Julian had a hand in it.