Cap's heart is unmatched, but Hulk's limitless strength makes this a fight Steve can't win.
Steve Rogers would never back down from this fight, and that's both his greatest strength and the reason he'd lose. Captain America is the peak of human potential โ but the Hulk transcends human potential entirely. Hulk's strength literally has no ceiling; the angrier he gets, the stronger he becomes, and there's no documented limit.
Cap's vibranium shield is his only real equalizer. It can absorb any impact Hulk dishes out, making Steve temporarily invulnerable to Hulk's strikes. But defense doesn't win fights โ and Cap's offense simply isn't enough to damage Hulk meaningfully. The super-soldier serum puts him at maybe a 2-ton lifting class; Hulk has held tectonic plates together.
Cap has 'beaten' Hulk in comics, but always through calming Bruce down or appealing to his humanity โ not through physical dominance. In a fight where Hulk is angry and committed, there's simply no version where Cap's physical abilities are enough.
Captain America's shield is nearly indestructible and can absorb Hulk's blows. His tactical genius means he could use the environment to his advantage, and his inspiring leadership has literally calmed Hulk down in the comics. Cap fights smarter, not harder โ he'd look for ways to end the fight without trading blows, possibly by reaching Bruce Banner within.
The Hulk can crack continents with his fists. A single direct hit from Hulk would end Captain America, shield or not โ the force transfers through Cap's body even if the shield absorbs the impact. Hulk is also faster than he looks, able to cover ground with massive leaps, and his healing factor means Cap's attacks do zero lasting damage.
Hulk wins through sheer, overwhelming power. Cap could survive longer than most thanks to his shield and tactical mind, but he has no path to victory in a straight fight. The only way Cap 'wins' is by reaching Bruce Banner's humanity โ which isn't really winning a fight, it's winning a conversation.
Captain America also fights
Hulk also fights