Hi Alex,
I didn't apply to GW, so I can't speak about that. I did get accepted at SAIS too and will be in DC for both years. I have similar interests as you, but definitely want a more quantitative/econ heavy IR program. That's why I like SAIS. It seems like we will come out of the program with really strong econ and quantitative skills, which, in my opinion, seems like an advantage in this current job market.
I know that SAIS is probably the most reputable school in DC (Georgetown is comparable), but I can only say that from what a relative, who works in DC and in that field, told me. In addition, SAIS has a great name within the IR community. I have also heard that the SAIS alumni network is excellent, with many SAIS alums willing to help SAIS students in whatever way possible. One con that many people on this website have said is that SAIS is nowhere near the Hopkins campus which means you can't take classes at other colleges within Hopkins.
I would say SAIS is the way to go, but at the end of the day, it's what you do with the degree and your time in grad school that really matters. And you seem to really like the program at GW!
For me, I'm leaning towards SAIS but it's still a toss up between that and SIPA.