Let me start by saying that both are great tools and enable you to collate materials quickly and efficiently. The big plus point for Flipboard is how cross platform it is with you being able to collect data from apps and browser click-ins. You can easily select materials as you go. It also makes a beautiful magazine that you will enjoy reading. However it does not always put things in the order that you would like them. It's like you are the writer of the magazine, but it is the editor that lays it out and decides the order.
On the other hand Storyboard enables you to easily compile your entries together at the end of the event and put it in the order that you would like.
So when I did my week running #AsiaED, I did both:
Flipboard version:
http://flip.it/E4UfH
Storify version:
http://sfy.co/byXK
On this occassion, I prefer the Storify, because the narrative stays in place, but for Learning 2, Flipboard worked very well and I was able to do it as I went along, which was brilliant!