Why would you poison a city's water when you can foment unrest instead? Both have the same cost, and unhappiness has double the effect of unhealthiness.

Because an unhealthy city is harder to counter.
Unhappyness has an easy solution: raise the culture %.
On the other hand, what are you going to do if your city is starving because of unhealthiness?
Except rushing health buildings (which is not always possible), there's no solution.

Therefore, your city is more likely to lose populations if I poison your water than if I foment unhappiness.

Good point. However, raising the culture slider has economic consequences across the entire civilization, and is a pretty drastic "fix" for a problem that affects a single city.

I suppose if they're running Hereditary Rule, unhappiness is extremely easy to counter, though.

Does somebody here use spies at this effect ? I don't see the point and like keeping my espionnage points to revolt cities to conquer them more easily. IMO espionnage needs some optimization because you can go along the game without using 90% of these features.

How are revolting cities easier to conquer?

Because they have no defense bonus.

I poison cities if I am going for a diplomatic victory and I am close to winning and I can knock down someone who is voting against me by poisoning like 8 of their cities. Or if I am close to domination it helps my population percentage to go up. It only needs to be that way for one turn for it to count.

There are occasions where I want to cause some hate & discontent with a neighbor, without a DoW, or because his spies are running around MY territory getting caught at their shenanigans. I'll usually run a couple counter-spy missions, then if that doesn't work, we start returning the favor and poisoning water supplies and stirring up trouble in random cities, not just the ones near my borders.

I agree spies need work. I often totally ignor them, apart from the great wall great spy steal early techs strat. I will however at the end game in a tech race for space or the better army unit send a fleet of spies to a rival like zara who cattages like crazy and destroy any and all cottages i can see, that slows the buggers down for a while and its cheap to prodcue spies and to destroy an improvement so you don't even need a percentage on the slider to have enough points to do it, bargain. The only prob is getting acces if they are on another continent and you don't have open boarder but often another civ will oblige and you can eventually get across land.

I rarely if ever forment or poison

I poison cities if I am going for a diplomatic victory and I am close to winning and I can knock down someone who is voting against me by poisoning like 8 of their cities. Or if I am close to domination it helps my population percentage to go up. It only needs to be that way for one turn for it to count.
Wow, doesn't that take a lot of spies and espionage points? Wouldn't it be easier to do this job with soldiers, and just take a single city outright?

Poison > Foment Unhappiness in globe theatre city at least

Good point. However, raising the culture slider has economic consequences across the entire civilization, and is a pretty drastic "fix" for a problem that affects a single city.

I suppose if they're running Hereditary Rule, unhappiness is extremely easy to counter, though.

Based on my experience, if you have a few key improvement in targeted city, simply raising the cultural % at 10% is often enough to stop starvation (growth is stopped for a few turns, but that is no big deal).
The economic hit is pretty insignificant. Running at 10% for a few turns is hardly an economic problem.
If you have to keep it at 10% or 20% because your cities are constantly targeted by foment unhappiness, then your problem is your "spy defense".

I personally never lost a single population point with foment unhappiness, but lost many population points with poison water.

EDIT: This is less relevant since the last patch, but it can still be useful: the best solution to spy induced starvation is often city placement. Sounds weird maybe, but think about it: if fat crosses overlap, you can redistribute the shared tiles in order to give new sources of food to your targeted city. Of course, stopping spies is not a good reason in itself to overlap fat crosses, but it is worth giving a though when planning expansion near your enemies' border. Juggling with fat crosses tiles is how I survived a marathon game pre-3.13, where there were many spy missions directed toward my Empire.

Poison > Foment Unhappiness in globe theatre city at least

I was about to say never, but then saw this. I would say that that is the one exception to the rule.