ah64id - of course, generator is not charging the battery, it's running the charger that is charging the battery. Didn't know that anybody needed explaining that.
And - no, generator is not as efficient for charging as shore power.
When load goes down, with shore power you only use what is needed.
OTH, fuel consumption of generator doesn't drop proportionally to reduced power. When power drops 4 times, fuel consumption only drops 2 times. When power drops below 1/4 - in those last slow 10-15% of SOC - I am not even sure that fuel consumption would drop any further. Less fumes - don't know, smells the same to me. It may draw 5A current but would still need 0.07 GPH. I can even tell you more - it will still use a fuel when there is no load.
As to those 59-53 DB numbers - they are manufacturers numbers, and I wish they were true. For Eu2000 at 25ft it's usually in the mid-60s or low 70s with minimal or no load and "Eco" On.