I'm sorry if you felt that was rude, but this is a fantastically bad question because neither of them will set you up for your goals. You want to end up in NYC following graduation, you're international which means you'll be taking out private loans in order to attend, and you're talking about paying full price at a school that places minimally at best in your desired market. Do you have family assistance in paying for law school or are you just fantastically wealthy? Will you require an H1B visa to practice in NYC?
GW places ~35-40% of grads into jobs that will likely sponsor a visa (if you need one, but I'm assuming no green card marriage or other path to being here for now). That's a horrible financial gamble to begin with because you're talking about paying $308k (or whatever GW is at sticker) for at best a 40% chance of reaching your goal. If you understood how the forced curve of law school works, you'd understand why that's such a fantastically poor decision. Layer on top of that a desire to practice in NYC, where neither UW or GWU place any large percentage of grads following graduation, and you're cooking a recipe for financial disaster.
Forgive the lack of using kid gloves, but unless you have the freedom to throw hundreds of thousands of dollars of free cash at a below-mediocre shot of reaching your goal, going to either GW or UW would more than likely be financial suicide. Why do you think either of these will get you to your goals?
Please see the below website regarding the placement power of GW and UW. They will not put you in NYC following graduation. I'm sorry.
https://www.lstreports.com/compare/gw/washington/