Their big advantage is planetary development coupled with powerful ships, starbases and diplomacy/influence
It thought the asa are slightly overpowered in 1.9a, due to their fortress like ship classes ^^ they breed their best ships on one special planet with appropriate buildings.
Generally soldiering is quite strong. Asa are designed to be defensive in nature, but have a few other options as well. If you research ethics and choose evil, you'll get eg. spore tech
However, a tweaked version is coming probably in the beginning of next year