The underground greenhouse, has no expensive clear sides (plastic or glass), a cheap plastic sheet roof to let in more light than glass, and heat loss through walls to the air, which can be colder than the ground (57 degrees Farenheit or so), so it will be cheaper to build and run. 

Of course, it's a lot of digging, and the left over dirt must go somewhere.  Hint: Save the top 10 inches of top soil when starting to dig for use in the greenhouse.