"The Phantom Menace" ends with Obi-Wan as a full Jedi Knight and Anakin as a Padawan. A decade later, "Attack of the Clones" ends with Anakin's marriage and the beginning of the Clone Wars. Following that, the series "The Clone Wars" covers the three-year gap between "Attack of the Clones" and "Revenge of the Sith." Given the amount of ground the series covers, it has to be inferred that when the First Battle on Geonosis happens, the war begins, and Anakin is immediately promoted, as Obi-Wan and Anakin are both generals in "The Clone Wars." From that point, Anakin pretty quickly gets assigned a Padawan in Ahsoka Tano, who, by the way, also leaves the Jedi order — maybe the Jedi Order needs to wait for a little before giving newly-minted Jedi Knights apprentices?
From that time on, Obi-Wan and Anakin are basically colleagues on the same level, as they are generally given the same level of responsibility in most situations. Often they would lead their own platoons in the same battle, with neither outranking the other. Not only had Anakin just been promoted, but he started his training considerably later in life than most Jedi, considering that he was almost denied entrance due to his age. If Anakin had bristled at Obi-Wan's instruction before, no doubt he really resents any perceived seniority by this point. Obi-Wan, however, never seems to begrudge the fact that Anakin skips ahead to become his equal.