Running watts of a Honda 2000i is 1600. Surge watts is 2000.
Micro Air's easy start, thread linked below, reduces the starting current of a typical AC 50% or more making it possible for a Honda or other 2000 watt inverted start a 13,000 AC.
One person in a motor home can run his 13k btu AC on his BATTERY
BANK FOR TWO HOURS USING AN INVERTER with his micro Air easy start.
As far as hard start capacitors like a Supco most newer AC's come with a hard start cap installed already taylored for that unit. A Supco cap on my dometic AC actually made starting it worse.
Nobody that has installed a Micro Air easy start has been disapointed, they're actually thrilled, with the results. Here's the thread. I suggest you read it and the generator
shootout that's mentioned too.
Further the hotter the temperature the harder an AC is to start. 90 degrees seems to be the breaking point. With Micro Air's easy start makes it easy to start.
And the BTU rating does make a difference, it takes a larger compressor that draws more current for more BTU's.