The amount of responsibility they gave me, I was able to take on so many cool projects that I would never be offered as an intern at a big corporation. I even got to be a real part of pitch meetings, and all of my superiors were so kind and encouraging.
What I wish was different
It was an unpaid internship which wasn't ideal, but because of that they were really flexible with my work schedule and how much I could take on.
Advice
With nonprofits especially, just ask for the position you want! They likely need all the help they can get in whatever area you're interested in.