If I recall correctly, captured cities (of either kind) have 1 unhealth per pop, compared to only 0.75 unhealth per pop of your own cities. On top of that, there is a (flat?) amount of unhealth added for whether it is annexed or puppeted (with puppet being a smaller amount) - however, this fades over time. Then, of course, there is the 4 unhealth base for a city.
The result is that at best you can reach near neutral (but never quite) local happiness from a captured city, with possibly virtue global health being created as well. So, at best, a captured city might not hinder your health - but it wont really help it, either. Even considering the best case, a captured city will add a fair amount of unhealth for a fair period of time until the annexation/puppeting unhealth fades away.
Also, take into account that puppet cities are going to likely require a fair amount of biowells to cap local health since you have no control over the buildings - even then, the governor might not work those tiles and you may have issues expanding the borders since you can not build culture buildings nor purchase tiles.
Since health is so important now for non-domination, capturing cites therefore tend to come down to three reasons, in my judgement:
- You have a lot of surplus health and thus don't care about the unhealth since it wont hinder you. Unless it is a big city you are capturing, though, it may just be easier and more effective to just settle a new city instead - sort of depends on whether space is an issue or not.
- You really need to remove that city from an opponent (probably best to raze in this case, though); usually this is because they're are going to beat you to a victory condition and this is the only (or best) way of stopping them.
- You are going for a domination victory and are just ignoring health altogether. It is sort of hard to not ignore health when going domination as there is little prospect of staying healthy if you are capturing many cities (especially in the short term).
