Both simply involve a style of cooking. Using the lid down creates a better flavour and a moister meal. There are other cookers around that also involve lid down cooking.
We went for the Ziggy as it gives a larger cooking area, higher heat output (to be able to cook with the lid up), and more importantly because the lid folds back under giving it a smaller packing size than the Webber.
Both units are now made in China, the Ziggy is exclusive to BBQ Galore.