It's a tough call.
The Azdgari offer the shield generator, which, combined with the exp. shied generator, make the Azdara almost invincible. They also have the Azdara bay and Azdgari upgrade, both of which are useful on large warships. Of course, depending on your ship, you might not use the Azdgari upgrade or the bay.
The Zidagar have the Zidara, which is one of the best ships in the game, being both maneuverable and well armed, as well as having 2 Zidagar fighters. The extra 20 tons they give you is also very nice, especially if you have a fighter that starts with limited weapon space. The phased beam is not very useful, as it drains your fuel quickly and takes up a gun slot. It also can't be sold in version 1.0.1. The best thing they give you is the Zidagar ECM, which basically makes you immune to all guided weapons but needle missiles.
The Igadzra give you SAE modules, as well as the Igazra, which, as we all know, is the strongest warship in the Crescent. They also offer the Plasma Siphon, which is one of the best secondary weapons in the game, as it uses no ammo and does a lot of damage.
Overall, I would say the Azdgari, as an Azdara with both shield generators is nearly indestructable.