Ah. Hibernate writes to the Swap, and Swap needs to be big enough to hold the content of RAM. Hence, in your case, no Hibernate.
Suspend writes to RAM, and RAM needs to be big enough to contain the Desktop and its doings at the point of Suspending.
Try setting Suspend on lid close, and blanking screen after one minute, power unplugged. Sneak a peek under the edge of the lid after two minutes and see what's going on.
