There is a penalty for razing cities, which may or may not be larger than the bonus for having captured the city, depending how many cities you have already. But in the long run, it's better to raze than to keep marginal cities.
The victim does not lose any more stability for having the city razed (he'll lose some for having lost the city, but whether you keep or raze it doesn't matter for him). This probably isn't what was intended, looking at the code - seems the razing penalty is intended to go to the victim, not the razer. But it is the razer who gets the penalty.