A generator install ultimately involves a lot of different sub-contractors; Electrician, gas fitter, gas supply company, general contractor for pad, trenching, etc., maybe even a separate excavation company for trenching, and of course the generator dealer. Oh, and don't forget permits for construction, electrical, and gas.
So I think it comes down to who's going to be the GC, and who will pick the subs.
I expect that more full service generator dealers can also act as GC, and will use their own subs. Or maybe they can't be the GC, and will just tell you what the GC needs to provide for them to park the generator, and when to call them to do the startup after everything is hooked up.
Or you can find your own GC, and they will line up the subs.
Or you can be the GC, use your own preferred subs, and do all the coordination (cat herding) yourself.
If you have a strong preference, then go that route. Otherwise I'd start with the generator dealer, who might also be an electrician, as ask what your options are. Some may only want to GC the whole thing, some may only want to sell, place, and start up the generator, and everything in between.
When I installed one in a previous house, I acted as GC, mostly because I already had good relationships with gas and electric subs who I trusted and knew did quality work. Oh, and the generator dealer should be able to tell you what all the rules are for locating the generator. In my location there were limits on proximity to windows and doors, distance from the building, locations of power disconnectes, etc. Interestingly, the distance from the building depended on whether the generator was in a metal vs plastic enclosure, with metal allowing placement closer to the building.