They have a very large bonus to resources gained from pops, and their starports put ships together much faster. They also have a quite a few ranks of the repeatable techs, and they have their own special, different ships!
Each Awakened Empire type has 1 of 4 possible ship designs, depending what ethic they have.
Xenophobic has Kinetic, (they are the hardest to fight against too)
Xenophile has rockets,
Spiritual has Arc Emitters with rockets,
Material has Energy. (can be tough, but their designs aren't that good)
All 4 use many carriers.
For all I know, the Titans are the same, with super lazers of doom. I've never seen them field more than one of those yet.
They have crazy big numbers indeed, but their main weakness is that they always build the same stuff, and can be countered really hard.

We usually lose 1 ship for each 2 or 3 of theirs in evenly-matched 250 vs 250k encounters, and even won with weaker. ~60k vs ~120k was the best win!