My two cents:
Since I have a 15k BTU A/C, it takes at least 2000 watts to run it, and around 3000 watts to handle the locked rotor amps from the compressor. My 3000 watt Yamaha (which worked flawlessly until it seized last weekend) could handle it, but it was marginal... I had to make sure the refrigerator was on propane, for example. However, the Yamaha when running the A/C was quieter than two paired Honda eu2000s with a similar load. At idle, the Hondas were quieter.
I compared the Champion inverter generator... I really didn't notice any real difference in noise between my Yamaha 3000 watt and a 3100 watt Champion inverter.
Now, here is something I did learn. The Champion open-framed generator compared to an inverter is loud. When I fire up my Yamaha in my pickup truck bed, under a covered carport, which echos, it is loud, but not too bad. When I started the open-frame 4000 watt model from Lowe's, there would be no way to have a normal conversation near the unit whatsoever.
If I can't get my Yamaha fixed, I'm definitely going for a Champion 3500 watt dual-fuel model, just so I can run it from propane before I store it, and keep gasoline in it normally.