I have both, too and I use the Kindle more (or at least I did until the screen died) because of the slightly smaller size and weight make it more portable for me. In other words the Kindle fits in my purse better than the Iliad. I also really like the ease of getting blogs, newspapers, and magazines. Not a lot of variety but Amazon has what I regularly read.
A few other things I like about the Kindle is that it boots up much faster than the Iliad, it has a sleep mode, and it's very easy to get content wirelessly.
The Iliad has more potential, IMO, but I don't have the time and energy right now to learn how to make it work for me.