I think it very much depends on which weather service has a weather reporting station close to your home, depending also on the country you are in. Different weather services/bindings can vary a lot depending on the countries. Also how often the weather info is being updated on the server side etc.
I would not rely on info for rain or heavy wind gusts to close windows, as those events can often be very local and not being picked up by at all or very late by any weather service/binding. For those I would definitely recommend using local sensors.
Very similar for the temperature, but not as critical, although a cheap local temperature/humidity sensor would give you much better data as well.
I use weather services/bindings for more general info like forecasts, cloud cover etc.
For example, I’m currently comparing two different weather stations from OpenWeatherMap, which both are close to my home. From the data and charts I’ve created over the last days/weeks I can see that they do differ a lot on many occasion.
Hope this helps.