I have been happy with my 3000 watt Yamaha iSE (model with no battery boost, but electric start -- it has been discontinued, but shares parts with the other Yammy models). If you buy a SEB model, the 500 watts from the battery are enough to help with the locked rotor amps from almost all 13k BTU units, and a good number of 15k BTU units.
My Yamaha (knock on wood) has been running quite well, for over 3000 hours, with oil changes and other basic maintenance.
You can go with Honda twins, and I've compared my setup to what others use, and one can go either way. I like having a bigger generator because it actually is quieter than the Hondas when unloaded, as well as when handling the A/C and so on.
As for a Yamaha or Honda model, I might even make a recommendation different from the pack: A Yamaha EF4500iSE ($3059.19) or a Honda EU7000i ($4499.95) model. Yes, you will be paying 50% to 150% more, but you will be getting an inverter model that has the headroom to laugh at the incoming impulse current from the A/C, as opposed to bogging down, and undervolting the A/C's compressor. Plus, the bigger generator has the option of remote start as well.