"I think the inverter generator
(Honda 2000 type) is really hot on both the hot and common side so using "
There are a number of posts online about portable generators (including the Honda's) and what the proper procedure is for using them in "ungrounded" installations, i.e. marine
or portable use where the neutral and ground may or may not be connected to each other, and when a "true" ground may not exist.
There are reasons to do it both (either) way, including electrocution risks. As long as you're comfortable with the setup and understand what might happen, whatever floats your boat.