From everything that's been said by the designers, it seems like a district-by-district city capture is the most likely procedure - for big cities anyway. And will require a district-by-district defence.
For example, if Babylon is more advanced, you don't necessarily have to take Neb's cities, you can send in a swarm of troops and burn down his science buildings. If you harass the builders coming to fix them up, you could handicap his science output severely.
Because military units come from an encampment, if you seize that first, then the city can not make any more units to defend itself, and would rely on backup from other cities.
In addition, bombing an industrial area would set back an enemy's production. So it seems like warfare is really going to expand across the city tiles. Turtling with a few archers/Xbows/artillery or aircraft until the enemy runs low on units - then counterattacking - doesn't seem like such a viable strategy any more. They won't just pillage your luxuries and mines. Many of your buildings will now be out in the open and vulnerable, so you will have to defend your districts too.
Looking forward to it