My Honda 2000 will USUALLY start/run the Emerson 13. 5 a. c. unit on our 5er - but it's pretty obvious the Honda is under more strain than it's happy with, so I wouldn't really consider that as a normal operation.
The Yamaha should start and run a 13. 5 reasonably easily, and still some wattage overhead left in reserve - and if the A/C was a determining factor, I'd go with the 2400.
Other than that, my 2000 runs great, and is a BIG improvement over the 1000EX it replaced.
As to the heavier weight of units like the Honda 3000, why must they be removed from the truck? At least in our case, we could as easily leave it in the bed of the truck and run it there, rather than wrestle it on and off the truck.