What I get from the film, without regard to what other authors have added, is that the question of rank doesn't really matter. Lord Vader is not in the chain of command - he's nobility, not military personnel. Tarkin has command of the station, while Vader carries significant political clout. Thus, the two relate as equals. Tarkin is not afraid to get snippy with Vader, even to mildly threaten him. But when he demands that Vader "release him," there is no "yes, sir" in response. Vader replies simply "as you wish," deferring to Tarkin's authority because it pleases him, not because he has to. And he simply declares that he will face Obi-Wan - there is no asking for permission. There are really no formalities between the two of them at all, in fact - because they simply aren't in the same heirarchy.