Is a space heater or my window heating unit more energy efficient?
Looking at the unit you linked to (and your comment on waiting for the "cycle" to finish), it appears to be a heat pump. Heat pumps are typically more efficient than electric radiators (e.g. a plug in space heater). They lose efficiency as the outside temperature falls, and eventually you should switch over to emergency or electric heat, which should be built-in to this unit. This is identical to the heat source you would have with a space heater. I doubt you'll see more efficiency out of a space heater (it all depends on the individual units), but if you do, it wouldn't be until it's very cold out.

Side note: The point to switch to electric heating is somewhere around the freezing temperature. I've seen comments ranging from 40F to 20F, that that may also vary from one unit to another. Depending on the unit, this switch may be automatic, or you may have to manually enabled it. If you get down to freezing outside and can't get above 65F inside, then I'd manually flip to electric heat.