Fletcher strikes me as higher up the food chain than GWU. I have a couple friends at Fletcher and they love it and have access to a lot of amazing internships and jobs. The students and faculty are amazing. Also, don't underestimate the value of being able to interact with MIT, HLS, HBS, and the rest of the Boston community. DC may be the policy epicenter, but in terms of the cutting edge, Boston is where it's at. Far more top-level programs there.
Looking at your signature -- I see Fletcher, SAIS, and MSFS all accepted you -- I would put those in the same echelon (the top one) -- and Fletcher was kind enough to give you money.
Duke is basically in the middle of nowhere. You're not going to have access to a larger dynamic community like you would in Boston.
And as for GWU, from interacting with various people at the program I will say that my sense is that it's not on the same level as Fletcher. I could be wrong on this.