So, the faculty told you deferral was a possibility when you applied, but now the graduate school is telling you otherwise? Have you spoken with faculty since receiving the Fulbright award? What did they say?
So you've already lived abroad in your Fulbright country, or was it a different country? Do you think there would be an opportunity to apply to a research/study Fulbright during your grad program?
I'm having a similar (but not quite as torturous) dilemma myself. Wait listed at an awesome, fully funded MFA program in the Midwest whose acceptance rate is <2%, but was also awarded an ETA in Italy for next year. I have another Master's degree already though, and I've always wanted to live abroad (never have) and become bilingual. Removing prestige (in my field) and the corresponding implications for my young writing career, Fulbright seems to be clearly more in line with what I actually want to be doing next year. But it would still be very tough to say no to such an exclusive grad program (been kinda hoping for a deferral all along, but doesn't seem likely).
My rule of thumb: go with the choice that genuinely excites you more. If you can't figure that out, ask your friends/family. Sometimes the right decision is painfully obvious in the way you speak about the choices to your closest friends and loved ones. This is actually why I applied to Fulbright in the first place. I was so certain more graduate school was the next step for me, but a close friend told me I sounded way more excited about possibly moving abroad than I did about more school. Didn't take long to realize she was right.