In an evolutionary sense, the answer isn’t clear. A recent molecular study suggests Atta may be no more than a derived lineage within a larger Acromyrmex, and that our distinction is artificial.
But what if you just want to key a specimen to one or the other? That’s easier. Count the spines on the front of the thorax- the promesonotum- you’ll find that Acromyrmex sports three pairs, while Atta has just two.
As an exercise, see if you can identify the ants in the following images: