Yeah seems like a relatively simple maths/econ problem to solve for, given some parameters like local solar power per m2 in the various seasons, electricity use in the various seasons and time of the day, and LCOE of solar and battery storage.

My guess is the differences in either choice aren't huge, as both solar and battery storage keeps getting cheaper.

Having an electric vehicle can really help, also. It basically soaks up excess solar power of an outsized installation during much of the year (making the payback time on the outsized installation very good), and can be charged away from the house during a few low-chance bad winter days when the outsized installation is enough to power the house but not the car. Electric cars are charged fully about 3 times per month on average in the US, so working around that with smart charging is not a complex challenge in the next decade.