Project Winner: iBrainstorm
Sticky only allows you to create two projects before you have to pay. You can delete and start over, but that's a pain. iBrainstorm allows you to create at least six (that's where I stopped). Much more versatile if you are using it extensively.
Multimedia Winner: Sticky
Project Flexibility: Sticky
Even though you can only make two projects in the free version, Sticky allows you to make multiple pages within your project (one student was on page 534 before her teacher stopped her). With iBrainstorm, you only get one page per project. Very limiting.
Aesthetic Winner: Sticky
iBrainstorm looks boring. Just a plain brown background. Yuck. Sticky lets you change the background of your pages. Great for organization by color.
Writing Winner: iBrainstorm
You can add your own writing to iBrainstorm projects but not in Sticky. It's a nice feature if you'd like to interact with your sticky notes to draw comparisons, link ideas, or add your own comment.
Overall Winner: It Depends
I think both apps have nice features that the other should have as well. I'm quite surprised that the apps haven't applied those missing features to improve their apps. I would encourage your students to have them both on their iPads to use for different tasks. After all, they are both free.