I suspect you just had something wrong with that particular one -- I don't follow them closely, but I can't recall reading about inverter failures except yours -- Who actually made the McCullough generator? It may just be another Chinese knockoff as so many of them seem to be.
What kind of problems were you having with the Yamaha? Was it inverter-based?
BTW, there is a thread on RV.NET entitled "3000W Chinese Gensets Info" that is currently 720 pages (Yes, pages, not posts!) long and still going!
I personally prefer the inverter-based generators because they can loaf along at eco-throttle, sipping fuel, and then rise to the occasion with just enough throttle to handle the load -- A conventional generator has to maintain a fixed, relatively high, RPM to maintain 60 Hz -- In my own case, I would be just using one to charge battery
(probably handle that without even coming out of eco-throttle mode) and run a cube heater and potentially a small m/w. I don't have a/c. Of course, not all inverter-based makes have the eco-throttle.
With some, one also has the option to hook two together, something almost impossible to do with conventional generator.
I've camped near people with construction generators and you get what you pay for -- Unfortunately the neighbors pay part of that price -- When I am doing my first tour of a new CG, looking for a site, avoidance of construction generators is right at the top of my list.
Alexandra, the trick with getting a generator is to first assess your actual needs -- The key one is what it takes to START, not just run, your air conditioner -- That's best done by calling the maker with all the numbers and asking them -- Also, check to see if Soft Start kit is available to decrease that starting load. You might also post your a/c's exact details and see if anyone here has specific info regarding it and particular generators.
Both Honda and Yamaha seem to perform well, but Darwin's experience with Yamaha parts/service bears some serious consideration -- Personally, I would tend towards the Honda as I have known several people who have successfully owned them, but I also wouldn't turn down a good deal on a Yamaha. I did talk to a factory service shop guy who handles both a few years ago and he said Yamaha tended to have more mechanical problems than Honda, but their electronics were "bulletproof".