I would imagine the atlatl as a long range weapon of war they would be most effective, on mass a volley would be devastating I would imagine, and something like the English warbow, and a lot easier to make the darts and shoot for a period of time compared to spear or javelin. You'd probably have to strength train a fair bit to throw spears constantly.
Here's a quote from Wikipedia,
Grande do Norte in mid-17th-century Brazil. Anthropologist Harald Prins offers the following description:
"The atlatl, as used by these Tarairiu warriors, was unique in shape. About 88 cm (35 in) long and 3 to 4.5 cm (1 1⁄4 to 1 3⁄4 in) wide, this spear thrower was a tapering piece of wood carved of brown hard-wood. Well-polished, it was shaped with a semi-circular outer half and had a deep groove hollowed out to receive the end of the javelin, which could be engaged by a horizontal wooden peg or spur lashed with a cotton thread to the proximal and narrower end of the throwing board, where a few scarlet parrot feathers were tied for decoration. [Their] darts or javelins… were probably made of a two-meter long wooden cane with a stone or long and serrated hard-wood point, sometimes tipped with poison. Equipped with their uniquely grooved atlatl, they could hurl their long darts from a great distance with accuracy, speed, and such deadly force that these easily pierced through the protective armor of the Portuguese or any other enemy.".[11]
And I would of thought if you could hunt efficiently with the atlatl you were also trained and well practiced for war, perhaps a good reason to do so?