However, it is worth noting that Stormbreaker is more powerful than Mjölnir in that it can summon the Bifrost and is "The Thanos killing kind" but I don't think it's that more powerful on its own that it would be able to destroy the shield. Very easily, yes.
Is Stormbreaker stronger than Captain America's shield?
I think it is fairly safe to assume that Stormbreaker (being a cutting weapon, rather than Mjolnir which is designed to smash or build) would inflict similar damage to the shield as Thanos sword does. Conclusion: Stormbreaker minces Cap's shield.
Throughout Marvel Comics, the Hulk has tried and failed to break Captain America's shield but has never even come close, and since Superman is only a little bit stronger than the Hulk in his base form, it makes sense that Superman wouldn't be able to break the shield either.
Can Thor's hammer destroy Captain America's shield?
Ultimate Captain America uses a shield of pure Adamantium, although that metal may not possess the same properties in the Ultimate Marvel universe as it does in the mainstream Marvel Universe. The shield was destroyed when Gregory Stark smashed it with Thor's hammer, though Captain America would wield another later.
Captain America's Vibranium shield is one of the strongest weapons in the MCU, but some powerful tools can still break it! There are few items in the Marvel Cinematic Universe powerful enough to break Captain America's iconic shield.
But it doesn't compare to Hawkeye's arrows, Thor's lightning or any of Iron Man's weapons. Besides, throwing that shield is risky, since it might get stuck or lost. Captain America works best at melee range, which is fine, but in some situations, he's left with no solid options.
Although vibranium is susceptible to damage, it's depicted as the most durable material in the Marvel Cinematic Universe. The fact that Thanos possesses enough power to beak vibranium is a testament to the strength of the Mad Titan, but more importantly, the weapon itself.
Thor's hammer Mjolnir was defined by the fact that only the 'worthy' could lift it – so basically no-one except the god of thunder (and Vision, for some reason). But when it comes to the weapon's replacement, Stormbreaker – which Thor forges in Avengers: Infinity War – Groot is able to lift it too.
Stormbreaker has the additional power to summon the Bifröst, allowing Thor to teleport anywhere in the Nine Realms. Screen Rant has identified Stormbreaker as the more powerful of the two, based on this ability, as well as it being a much larger and edged weapon.
Although Cap's internal conflicts prevented him from being fully worthy to lift Mjölnir during Age of Ultron, Cap really almost pulled off stealing Thor's thunder.
Vibranium is just the strongest metal on Earth. In Endgame we see that Thanos' blade is able to break Cap's shield. There are much stronger materials in space, it stands to reason that there are beings out there stronger than it as well.
Swords, knives, and more have been used against Hulk and almost none of them even leave a scratch or mark on him. However, with that said, there are two bladed weapons that can cut into Hulk's skin.
Finally, after Logan tells him bones are coated with the metal, Hulk promises to strip it off his skin - but never successfully damages Wolverine's adamantium bones. Hulk has broken adamantium objects, armors, and weapons in the past.
Meanwhile, MCU Phase 4 saw Stormbreaker being wielded by Thor, Gorr the God Butcher, Love, and anyone else who was strong enough to actually lift and swing it. This is because of the respective origins of both legendary Asgardian weapons.
Stormbreaker can be used by anyone, it isn't bound by Odin's enchantments to only be lifted by the worthy. Mjolnir is, however, still enchanted, meaning that only those that are worthy may wield it. This applies to your last two questions as well. If you can lift Mjolnir, you can wield it.
It is NOT enchanted. Most people make this mistake but it was confirmed by the directors that anyone who possesses the ''physical strength'' to lift the weapon can lift it. How was Thanos able to lift both Mjölnir and Stormbreaker? He was able to lift Stormbreaker because Stormbreaker is purely about strength.
Many viewers have pointed out that Thanos was able to lift Stormbreaker without a problem, but this is because the ax isn't enchanted as Mjolnir is. Others believe Thanos lifted Mjolnir (although briefly) and have even argued that he would be worthy of doing so.
Both of them can beat each other in multiple ways! How does Thor beat Superman? By hitting him with Mjolnir really hard. Superman, like everyone else can be stopped if you hit him hard enough.
There's a chance it could be repaired -- after all, Mjolnir has been broken and remade on multiple occasions -- but seeing Thor break Stormbreaker willingly is still a shocking sight. By destroying Stormbreaker, Thor not only reaffirms how powerful he is, but he also shows Bill how determined he is in his new quest.
Mjolnir has been manipulated in different ways in Marvel Comics, and many years ago, Iron Man was able to hold the hammer… thanks to zero gravity, meaning that he didn't properly lift it and he would have still not been able to wield it on Earth because he wasn't worthy.
Is Stormbreaker stronger than the Infinity Gauntlet?
Thor had the element of surprise and a weapon capable of overpowering even the Infinity Gauntlet. Stormbreaker powered through the gauntlet's energy beam but left Thanos alive long enough to succeed, making his victory in Avengers: Infinity War all the more devastating.
Because without altering any continuities, if Fox's Wolverine and Marvel's Captain America were to come to blows, the claws would slice through the shield like a hot knife through butter. Vibranium can absorb kinetic energy, but it isn't indestructible (as evidenced by Thanos destroying the shield in Endgame).
Stormbreaker is capable of killing Thanos outright, and only Thor is currently worthy of wielding it. A head to head match up between Thor at full power and Thanos, even armed with the gauntlet, seems to favor the God of Thunder.
Physically they're pretty evenly matched, but Thanos is just a much more skilled fighter. No stones were used in the fight. Per Joe Russo: "I would say that he's just that powerful," said Joe Russo.
