The Honda 2000i is rated at 59 dB at full power. This spec doesn't mention at what distance.
I believe the low-noise reputation that Hondas have comes from running them at very low power levels, so noise output is less than 59 dB at lot of the time they're being used.
I've heard 2000i Hondas at full power and they do seem to make a lot of "racket" running at full power (over 4000 RPM).
We use a small non-inverter Honda some when camping, but it's an obsolete Honda model that is only 54 dB loud at it's full power (fixed 3600 RPM).
Click the Specs tab at this link:
http://powerequipment.honda.com/generators/models/eu2000i