This may be "N-Words" by Ted Kosmatka
THEY CAME FROM test tubes. They came pale as ghosts with eyes as blue-white as glacier ice. They came first out of Korea.
As a group, they accumulated wealth at a rate far above average. They accumulated degrees, and land, and power. The men—beginning mostly during their youth, and continuing after—accumulated women, and subsequently, children. And they accumulated, finally, the attentive glare of the racists, who found them a group no longer to be ignored.
Their bones are different than ours. It is not just their big skulls, or their short, powerful limbs; virtually every bone in their body is thicker, stronger, heavier. Each vertebrae, each phalange, each small bone in the wrist, is thicker than ours. And I have wondered sometimes, when looking at those bones, why they need skeletons like that. All that metabolically expensive bone and muscle and brain. It had to be paid for. What kind of life makes you need bones like chunks of rebar? What kind of life makes you need a sternum half an inch thick?
During the Pleistocene, glaciers had carved their way south across Europe, isolating animal populations behind a curtain of ice. Those populations either adapted to the harsh conditions, or they died. Over time, the herd animals grew massive, becoming more thermally efficient, with short, thick limbs, and heavy bodies—and so began the age of the Pleistocene mega-fauna. The predators too, had to adapt. The saber-tooth cat, the cave bear. They changed to fit the cold, grew more powerful in order to bring down the larger prey. What was true for other animals was true for genusHomo, nature’s experiment, the Neanderthal—the ice age's ultimate climax predator.
Thomas growled and let himself be pulled along, and someone spit in his face, and I saw it, the dead look in his eyes, to be spit on and do nothing. And still David pulled us toward the safety of the building, brushing aside the curses of men whose necks he could snap with the single flex of his arm. And still he did nothing. He did nothing all the way up to the end, when a thin, balding forty-year-old man stepped into his path, raised a gun, and fired point blank into his chest.
I found it by searching for science fiction short story neanderthals are genetically superior
The Neanderthal are not superior in every way, but they're superior physically, dominating sports, and on par with us mentally, with extremely good memory.