My bet is they are in fact less efficient than the more commonly used filters available. I see no reason why the media moving should filter any better than media that stays in place. In fact, for any given volume of media space, having moving media would mean there has to be less of it than if the entire space was filled with stationary (but properly porous media).
They way they are BETTER than normal filters is in their design for removing Ammonia and Nitrate.
With the media moving, only the strongest bacteria survive, and all the dead bacteria are knocked off, making room for new bacteria. In a normal filter this only happens when you 'clean' the filter.
These systems are used by sewage companies to remove the ammonia and nitrate from raw sewage and has been adapted to work in Koi ponds using the Nexus pond filters.
They work the same in tanks too, but their currently isnt a company making them commercially so its all about the DIY filter.
I run several of these throughout my fish house and they are great, I have two large-ish running in my 120gallon tank and the ammonia and nitrate is always 0, you still need to do water changes though to remove nitrite.
But you dont have to worry too much able the uneaten food in the tank causing ammonia spikes as it just doesnt happen with these filters. Nexus provide a full over view of how these systems work on their website, and its basically the same for DIY internals.
Hope this helps clear up some points.
EDIT:
here are some more videos, even a filter with a sponge in it for removing large waste perticles:
and a continued video
