I went two tailgating seasons trying to power my rig off of two Champion 2,000w Inverter/Generators with a parallel kit. Although they were rated at 2,ooo w you never really got that much juice out of them and combined I think was generating only 3,600k. The two would power the rear (15k) AC unit and maybe a few lights and the TV, but if the converter kicked on or the water pump, it would trip the genset every time. The frustrating part was that the front AC was a 13.5k unit that you'd think would run fine with a little extra to handle the converter or water pump or an extra lite here or there, but with everything turned off, the two gens would never run the front AC?? Even installed the hard-start capacitor that is recommended all over the RV forums and still no luck...
I really like the portability (only 44lbs) and stackability of the Champions however, with a 50 amp service and the kind of heat we have this time of year (first tailgate is end of Aug and forecast is for 98 in Norman!) they were just not sufficient, so I bought a 5,600k inverter/generator to power whatever I needed while boondocking. It's heavy (144lbs) but a crane I ordered from Harbor Freight and installed in my truck bed makes lifting it in and out of the truck a one-man job.
Trial run this weekend and it powered both AC units, however, it struggled at first to kick over the front AC unit? Everything else ran well - with the AC running it powered the microwave, coffee maker, and hairdryer... not all at the sametime. If you need to run the AC and would like to run other appliances my experience has been that the smaller inverter/generators are great for tent camping, pop-up campers, and other smaller applications, but these rigs just have too much power demands that you'll want or need to operate and a larger generator is the way to go.