I think the choice is highly individualistic. I have had an iPad for a long time. A few years ago, I bought a Kindle at the urging of my husband, who was very seduced by the "non-backlit screen" argument and convinced me it would be much better.
I tried the Kindle for a couple of days, and ever since then, it has sat in a drawer. I really dislike reading with it and strongly prefer my iPad, go figure. Why? In my case, there are a few things. First, I don't like holding the small object for some reason. And I don't like that the screen is so small. I read very quickly, so on a Kindle, I feel like I'm turning pages like every other second. I'm also nearsighted, though, so changing to a small enough font that it would take me longer to complete a page means I have to hold the thing too close to my face to be comfortable.
The iPad screen is larger, and I just like reading on it much, much more.
My husband, on the other hand, likes the Kindle fine.