Fulbright vs. Consulting

Hey guys! I am a current senior at an Ivy and will be graduating this month. This fall, I accepted a FT offer to work at a boutique firm. I don't want to say the name here since they are relatively small, but they are top 20 by Vault's rankings for NA. Pay is also very solid, generally in line with MBB.

Though I was happy with the offer, I decided to take a shot at a Fulbright. This past week, I learned that I received the award. The award is a UK Study Award, and I would receive an economics-related master's degree (paid for by Fulbright) at a UK university and would conduct a bit of research. The degree would only take one year to complete, meaning I would be done next September. Obviously, it is an incredibly exciting opportunity. 

I am looking for advice on how to think about this situation. Right now, I am heavily leaning towards accepting the Fulbright. Generally, I think that the Fulbright is a more prestigious opportunity and may open different doors for me. It may also be a more fulfilling experience. Am I right? Is Fulbright more prestigious? How will recruiters/people in the industry view the Fulbright experience if I decide to come back to consulting? 

I am also thinking about asking the firm I have a FT offer with if I can defer my offer and begin next year. I suspect they may be open to this, but I am a bit afraid to reach out as I never let them know that I had applied to Fulbright. I will likely email them about it this week. Does anyone have any advice on how best to go about this?

General advice and comments also appreciated!