Actually, power consumption does NOT depend on fridge size, especially on the newer ones that are highly insulated. Now, there's probably a significant difference in say, a dorm fridge, and a huge sub-zero, but I noticed there's not much diff between that dorm fridge, and a 12 cu/ft fridge.
Refrigerators made in the seventies and a little bit before and after seem to be the worst energy hogs. They had small amounts of insulation in them, and compensated by using fans, which consume energy in their own right. Prior to this era, most refrigerators had natural-draft rear condensers. During this "energy hog" era, most manufacturers went to bottom condensers. This is a double whammy. Not only do they radiate their heat back into the food compartment, but they also nee a fan to move air over them. Inside, the manufacturers hid the coils behind panels, and used fans to move air over them.
Although modern refrigerators are better with energy than some of their older predecessors, they are still have some design flaws that keep them from being as good of performers as they could be. We've taken one step forward, but two steps back.
Some of the non-popular brands like sunfrost and Equator go back to natural draft like Ken describes, and was the defacto standard in the 50's and before. I believe Fridigaire held onto natural draft condensers well into the early 70's, although some of their interior evaporators had draft fans.