Size - Although Atta are tiny, and you may think they take up less space, think again. Atta create much larger colonies that Acromyrmex and some monstrous soldiers. A fully grown atta colony may even take 5x the amount of space compare to an Acromyrmex colony!
Jaw power: Atta are much more powerful biters, and i know from being bitten by both Atta and Acromyrmex. An atta minor bites almost harder than an Acromyrmex major!
Workers Sizes: Atta definitely wins this one. With over 20 castes within the colony - and an impressive soldier troop - Atta are sure better than Acromyrmex to watch.
Cost: Atta cost more than Acromyrmex, meaning that you will get 'less value for money'.
Sensitivity: Acromyrmex will withstand a lot more than Atta. A recent example is my colony going without fungus for 3 days. A hard thing - no food. They took it relatively easily but im sure Atta couldnt cope.
All together if you have the time, space and money - Atta. But if your looking for an easy, cheap and 'beginner' leaf cutting ant species to start with then go with Acromyrmex Octospinosus. Hope this helps