OK as far as a 4k vs a 5.5k generator, in some if not most cases the 4k generator will be on a 30amp unit. Now depending on the manufacture of the unit will depend on how well it can handle the AC and how well it cools the house.
I had a 2003 33V Suncruiser that was only 30 AMP with Basement air(2compressors) and a 5.5K generator. It was setup in such a way that 30 amp was plenty during the hottest of days with the AC going. Insulation mad a big difference and how they routed the air ducts throughout. My 5th wheel only had one AC and a 4k generator and would keep the place at 70 in the middle of July in South Carolina. Oh yeah I was running on 15amp service because I plugged into someone house. Didn't have to run the generator. Again it's how it built.
My current setup is 50 amp with 5.5k generator but last summer I was in a park where I only had 30 amp service and had no issue running both AC's and keeping it cool.
Are you getting the theme here, it all depends on the manufacture and how they set it up just for these situations. Winnebago does a good job with their power management system which will load shed to keep the important things going, AC. It's all in how it's built.
50 amp is better but you better be prepared for less, because it gets hot out there when the electricity goes out.
1 15k AC in a 30 footer may work just fine, some have an option to install a second 11.5k or 13k in the bedroom. You might need it you might not.