For the majority of Thor's appearances in the Stormbreaker. Although Stormbreaker was deemed stronger, Mjolnir still stands as the more important weapon to Thor and the entire franchise.
Leading up to Iron Man 2's post-credits scene when Mjolnir was found by S.H.I.E.L.D. at the bottom of a crater in New Mexico. In Thor's first solo film, Odin felt like his son was unworthy of wielding Mjolnir, so he enchanted it by proclaiming "whosoever holds this hammer, if he be worthy, shall possess the power of Thor." He eventually proved his worthiness and carried the mystical mallet against various foes. The hammer, which was forged in the heart of a dying star, was thought to be indestructible. Not only was it used as a melee weapon, but Thor could also use it to summon lightning, fly, or manipulate energy.
Hela ended up destroying Mjolnir in Battle of Wakanda, showcasing the fact that it enhanced his powers. It summoned the Bifrost Bridge and withstood blasts from the Infinity Stones. Thor also used it to impale Thanos in the chest and later decapitated the Avengers' most dangerous foe, but Mjolnir always served a bigger purpose.
Mjolnir Is More Symbolic Than Stormbreaker In The MCU
There was no doubt that the MCU proved the fact that anyone could wield Stormbreaker, only those worthy enough could pick up Mjolnir. Captain America was one of those candidates and Thor allowed him to wield the magic hammer on the battlefield. Thor kept hold of Stormbreaker since it was the stronger of the two but that didn't mean it was the more meaningful weapon.
After defeating Thanos, Captain America went back in time to return the Infinity Stones back to their rightful spots among the timeline. While doing so, picked up the weapon. It may be weaker than Stormbreaker in the Marvel Cinematic Universe's lore, but Mjolnir carries the bigger legacy since it holds a deeper meaning to Thor and anyone was worthy enough to wield its power.
