Do Empire Cities and City-States have the same amount of health?

Solution 1:

All cities start with 200 hit points, regardless of who owns them.

The city's hit points can be modified by certain improvements, like Walls, which add additional hit points to the city.

Additionally, the city's combat strength can make it easier or harder to do damage to those hit points. The combat strength is also modified by defensive buildings like Walls, but it is also bolstered when a combat unit is present in the city.

There are also World Wonders, Social Policies, and other benefits you can get which modify the defensive strength of cities and the modifiers of these improvements, which are tangential to your question. Just keep the combat strength and hit point variables in mind when you're looking at your potential policies, wonders, and so forth.

Some of this may be dependent on what expansions you have active, and occasionally things are balanced by patches to the games. I'd suggest looking at the tooltip for Walls, for instance, as well as checking the Civilopedia article for City Hit Points (Press F1 or hit the "Help" button in the upper right to consult the Civilopedia)