If you get a pizza in a regular box, then you just throw the cardboard away. But also, you have to use plates to hold your pizza. If you use paper or Styrofoam plates, you increase the amount of waste produced by eating the pizza. If you use regular plates, then you must wash them which increases waste water that must be processed. If you don’t want to fit the large box in your fridge for the leftovers, then you might use aluminum foil to wrap it in which increases waste, or you might use Tupperware to store it which must then be washed later thus increasing waste water. Not to mention you would probably use hot water for washing the dishes which increases energy consumption via your hot water heater, and if you use a dishwasher, then that further increases energy consumption.
So, when you really think about it, it could make an impact of sorts in both reduced waste and energy consumption.