Even without considering the inverter aspect of it, sizing a generator for a starting motor can be tricky. Go big and don't worry about it. But when you're cutting it close a lot comes into play.
Motor side : 1) Inrush of motor: For a given horsepower, different types of motors will have different inrush. (Example: A high efficiency motor will have a higher inrush than a standard motor.)
2) A variable torque or constant torque load. Being a pump, the mechanical (water) resistance is near zero when it starts (vs. say a rock crusher where there's immediate torque required at start up.
Generator side: Things that can vary from one-brand to another: 1) There's a flywheel effect of the genny's rotor and motor that will help overcome starting surge.
2) The responsive-ness of the governor to react can vary.
3) The fuel type (gas, natural gas, diesel?) The different power-torque curve of each type of engine will respond differently to overcoming starting surge.
Most (bigger) generator manufacturer's have free software or a website that (if you know your load(s)) can calculate voltage dips (or voltage crash!) at startup.
The starting sequence of your loads can also effect if generator sizing. Example (making up numbers here) a 100 amp genny might be able start a 50 amp motor and then run (3)- 10 amp loads. But if those (3) 10 amp loads are already running, it won't be able to start the 50 amp motor because of the starting inrush. This is important to know if a bigger load (like a pump) is cycling on and off.