When figuring out what to do with a captured city, here's a guideline: Occupy - higher science output (good for big cities). Puppet - better policy generation (efficient for small cities). Raze - when short on happiness, and the city is very undeveloped. What we consider "big" or "small" depends on circumstances of the game and our overall strategy. Small cities with important resources we need to develop might be more desirable to occupy than they otherwise might be. Puppets also tend to not prioritize happiness buildings, so it's sometimes necessary to occupy a city to rush Colosseums or Theaters in it.