Ran our Honda EU2000 for the last two weeks about 1-2 hours daily for camping. Used it to recharge the camper batteries. Used about 6 litres of gas for this! I was sad to find out that the 2000 watts wasn't enough to power the AC in my new camper.
The EU3000 is rated for something like 13k btu AC units - a friend of mine has used one a lot at racetracks. Honda has a lighter weight 3kw unit, but it is not as quiet as the EU.
I went for overkill on my last portable generator, partly to handle AC loads. We don't use the AC in the trailer much, but esp. if I haul the better half to a racetrack in the middle of nowhere and it's a scorcher - I have it covered. BUT, it's a good idea to do some knee bends and warmup stretches before I go to load that larger one !
Rgds, D.