The stately and refined upper (both literally and figuratively) echelon of Ishgard, where the nobles make their fine home, is shaken, but has its own defenses. Even off duty and caught off guard, it contains many of Ishgard's finest warriors. The streets are cleared of noncombatants in record time. They take shelter in the Saint Reymanaud Cathedral under the guard of the Holy See's Knights of the Inquisition, or take their chances sheltering in their own homes. Regardless of where they find shelter, they nonetheless get out of the way so that their warriors are free to slay the rampant dragons in the wide open spaces
Other districts do not fare so well. The common folk do not build their homes of sturdy stone like their 'betters.' They build in flammable and much more breakable wood, and closer together, in cramped alleyways that do not lend themselves well to containing dragons that breathe fire. Worse, the shelters for the noncombatants are few and far between, making the counteroffensive more difficult, and significantly more costly. The battle is a vicious and deadly game of cat and mouse through twisting, flammable alleyways, civilians caught in the crossfire. Their defenders are few and far between, because most of the trained and outfitted warriors are busy above.
Nonetheless, this is Ishgard, and if there's anything that can bring them all together, rich or poor, it is dragonslaying.