Samhy has already linked to my description of both readers. I just went and edited a couple of details, explained them at the bottom.
I really like both devices but if I had to choose one I would definitely take the Cybook. Love the folder structure, touchscreen plus page-turning buttons and physical home button, night mode, much less to no bluish tint of the light, and it works in a ziplock bag for bathtub reading.
Two things drive me a bit crazy with the Kobo: there is no "back" function, so if a book is opened, I cannot go back to the shelf it is in but must go to the home menu, then back to the shelf. I didn't realize how often I'm doing that until the Kobo made it impossible. Also, adding multiple books is a pain when you want to sort them into shelves because you have to go through your entire book collection to find them before assigning them to a shelf or use the search function to find each. Only 5 new books are displayed right on the home screen. I'm pretty sure you could avoid that problem by using calibre though.
If you do get the Cybook though, make sure that yours is an exemplar where the LED's are not visible at the bottom. Some Cybooks with frontlight have that problem as you can see in this Austrian video with the Cybook on the right.
In a German thread I have read that some have this problem and some don't. The reader on display I played with at the shop did but the one I bought doesn't.
I have no idea if this problem is a frequent occurrence or not though.