Is there not some effect about whip unhappiness (present in the city that you raze) being transferred to the next city of yours?
I'm pretty sure that's not the case, because when I keep a captured city it often has whip unhappiness, but if I raze I never get unhappiness.
Perhaps if you abandon your own city any whip unhappiness transfers?
Pros: Razing can net you workers from 1/2 the city population and you avoid resisting citizens and otherwise having to cover an unhappy city that could culture flip away. You avoid inheriting additional unhappiness from the enemy's mistreatment of their citizens (whipping and drafting).
Cons: You lose wonders and non-cultural improvements in the city (don't think a rax, harbor and aqueduct is of negligible value), you have an opportunity cost of the population of the city not contributing to your empire, you have to spend food and shields to produce a settler to settle the lands of the razed city. It affects AI attitude towards you, but I'm not sure if that has any gameplay effect. There may be a small opportunity cost in delaying the connection of a luxury or strategic resource controlled by the city.
My enemies usually have higher culture, and I'm conquering cities closer and closer to their capital, so I often raze, take the free slaves and avoid the hassle of whiny foreign citizens, quelling resisters and culture flips. So I generally have settler pumps, food-rich cities dedicated to settlers or cash-rushed settlers in high-waste cities continually producing settlers to fill in conquered lands.
But as with everything in Civ3 it's situation-dependent and much will be decided by your play style and game goals.