The eu2x000 series generators have had a high (but within spec) no-load AC voltage output from day one. As the load increases the output voltage ramps down to the 120 ballpark at full load. My eu2000i no load output voltage is 127.1 with eco on, and 128.6 with eco off.
The 12 volt output is not only unregulated, it's unfiltered. My manual says the following about it:
"The DC receptacle should ONLY be used for charging 12-volt
automotive type batteries. The DC charging output is not regulated."
They should also have added to use it only on FLA batteries. Ripple kills AGMs.