The toothed belts don't slip. Nor do chains. There are pros and cons for each of the systems.
The Staton chain drive is more robust, handles more power, and handles abuse (jackrabbit starts, etc) better than gebe. It is a little noisier, and definitely heavier, though. Since the wheel sprocket freewheels, you can coast with just a background click-click-click sound, and can pedal the bike with no load from the drive system, without removing the chain. Although the Staton chain requires more maintenance than the GEBE belt, it is not exposed to the same amount of road grime as the bicycle drive chain, and, once aligned, it isn't affected by lateral movement, like that of a derailleur.
The Gebe system is lighter, and typically needs less maintenance. But, you have to pull the drive belt if you want to use the bike without the drag of the clutch. Granted, this only takes a moment, but you do need to stop. Belts are susceptible to damage/short life, if driving habits aren't more ... 'restrained' I guess is a good term. The gebe drive ring will take some work to get it aligned properly, so as to avoid vibration.
From an efficiency viewpoint, the GEBE system is probably slightly more efficient than the gearbox/chain combo of the Staton system. It's not enough to brag about, though.