A futon is a lightweight frame holding a special mattress, which 'bends' to form a seat and back. While it is similar to a sofa bed, it is usually composed of a exposed wood frame and mattress. The mattress slides up to become the back and seat. It has the same function as a sofa bed. However, it is lighter in appearance, since sofa beds are fully upholstered frames.
Either option will work. The comfort level of the mattresses and the overall appearance of the piece, then become the issue.
More about futons......
http://www.thefutonshop.com/ 'bi-fold - The length of a bi-fold frame sits parallel to the wall and opens easily by pulling the seat section out, the frame slides down into the sleeping position. Most bi-fold frames have three positions- sitting, reclining, and sleeping. You need approximately 81 inches of wall space and 54 inches of floor space to fit a standard double size bi-fold.'
Good luck on your project, Tom.