While it is true that propane has fewer BTU's per gallon than gasoline; I have run my EU2000i on propane for hundreds of hours and have neither measured nor noticed any reduction in electrical power output when switching between fuels.
The only times I have ever noticed a power loss is at elevations above 6000 feet... first time this happened I was in Flagstaff AZ and wasn't able to run the convection-microwave at full power :E This issue is the same with both fuel types, and I now know to adjust the fuel mixture when camped at altitude. The adjustment of the propane demand regulator is super simple, and for gasoline I carry two additional main jets in the TC with me and swap them out depending on my destination.
Here are sizes, approximate altitude ranges, and the Honda part #'s for the jets I use:
0.62mm, Sea level to 4000' p/n 99101ZG00620 (this is the stock jet size)
0.60mm, 2000' to 7000' p/n 99101ZG00600
0.58mm, 6000' to 10,000' p/n 99101ZG00580
I'll add that my Honda is 16 years young (12 of them on propane) and, other than a broken pull-start cord, I haven't had any reliability issues whatsoever.
-Mark