Sacred Haven of Debauchery

But it seems like even reducing the enemy's defense to zero and matching the army size didn't help much; there were some other bonuses for the locals.

Ment, I usually play a race with a trait that reduces army damage, but I didn't have any particular problems. I usually built slightly larger armies than the defenders. I would attach a general. And then I would buy army upgrades. Everything was captured quite easily. In the late game, you can have an assault fleet of 5-10 elite armies (psionics, androids, or supersoldiers), which is usually enough to conquer almost any planet without losses. I also recommend looking for planets with titans; then you have a chance to get the ability to hire up to three cheap but very tough and strong titans. And sometimes you can summon a ground version of an avatar for the psionics.