I have both a sofa bed and an air mattress, and I FAR prefer the sofa bed because air mattresses tend to be loud, cold, and always seem to lose air during the night. I actually just replaced my old sofa bed with a new pull out type, and I think the pull out is much better. The type with the bed part inside have mattresses that are necessarily thin, while pull out sofa beds use the seat cushion and back as the mattress and they have a lot of support. It means your sofa is firm, but I prefer that so it works for me.
This is the one I decided to buy. Good price, good color and fabric (I got the dark grey), lots of storage underneath (also great for small apartments!).
http://www.ikea.com/us/en/catalog/products/60301458/