Anytime you make a system more complicated and add more parts (ie. a transmission) to it you will likely increase friction as well. This increase in friction correlates to a decrease in efficiency.
I found this quote far down the page
Here
Internal gear hubs have a efficiency of 92% compared to 98% for derailleurs. These numbers are valid for new and perfect trimmed drivetrains!
Internally geared hubs like the Shimano 3, 5, 7 speed hubs are cleaner and simpler to operate so why doesn't everyone use them? 2 reasons. They are heavier and they less efficient than a derailleur style transmission. The difference may only be 6 percent between them but for many cyclists that would be 6 percent too much.
Our application is different however and other features such as gear range and durability are also important. I have found the Nuvinci to be excellent in both categories.
The Shimano style internally geared hubs may be 92% efficient but the Nuvinci is probably even less based upon the design. If you try to find hard numbers from Fallbrook they seem to evade the question and instead tell you to ride it and see for yourself. They claim that the ease of shifting and the ability to always be in the right gear overcomes any increased loss in efficiency. They may be correct.
As an example I have 2 bikes that are very similar. Both have 70cc (true) motors with the same hp modifications right down to the same style expansion pipe. Both have street tires and are well maintained. The biggest difference between them is that one has a Nuvinci hub and the other has a conventional derailleur. The Nuvinci bike has more top end and accelerates better. Now I know this doesn't make sense because of my statement that I thought the Nuvinci is less efficient. I get that impression from when I pedal them without being under power. The derailleur bike seems to take slightly less effort. So why is the Nuvinci bike faster? Perhaps Fallbrook is right and being able to always be in the right gear and smooth shifting counteracts any loss in efficiency. It is hard to tell but one thing I am certain about. If you are going to put a gas motor on a bike the decreased efficiency of the Nuvinci hub is more than made up for by all its other qualities.