The Honda base has well engineered anti-vibration feet, and the unit itself is also designed to isolate vibration. There are no ill effects with having it on the platform. Mine will usually run for 6-8 hours depending one how much juice we are pulling.
Advantage to the Honda EU2000i is it has a smart throttle that allows it to automatically throttle up and throttle down based on the amount of juice demanded. This really saves on the gasoline consumed and extends your run time.