Weather app: which is more accurate?

I live in Brooklyn (NY), and I don't know whether having Location Services or manually picking Brooklyn in the Weather app is more accurate. This may sound like a dumb question but with LS on it shows me the weather for New York. I don't know if it means Brooklyn, Manhattan, or the entirety of NY. I would rather not go out and before I get to whatever destination it starts raining when it says it's not going to rain for 2 more hours. Help appreciated!

(screenshots)