If you are doing a lot of reading I would never a consider LCD based reading device. The eyestrain is huge while e-ink is really easy on eyes.
Maybe one thing nobody considered here - the backlighting. I know it's very convenient thing to have but it is definitely not natural. When you're reading regular books and magazines, you automatically adjust your light so you feel comfortable (sitting close to window, turning on a lamp etc.) Ambient diffused light feels more natural and with E-Ink display, you have the best of both worlds - the portability of electronic device and natural feeling of regular paper.
Actually, studies have shown no difference between e-ink and LCD displays when tested over a group sample.
Personally, I did not like reading on my old iPad 2 at all, which led to me buying a Kindle 4. What I found was causing me eyestrain was not the fact that it was an LCD, but rather the grid over the screen caused by it being a
low resolution LCD.
Despite being a low resolution device as well, the Kindle avoids this because e-ink doesnt have this structure on the display.
However, the iPad 3 display doesnt have this grid over the screen either, and text looks considerably better than it does on the Kindle due to the higher resolution. I even went so far as installing custom fonts on the Kindle, because I wanted something that resembled printed books (I settled on Minion) but it just doesnt look as good as iBooks. Im disappointed you cant install custom fonts there, but the selection in iBooks is pretty nice.
As long as I watch the brightness of the LCD (too bright and it leads to eyestrain) and use the sepia tone, I can read on the iPad just as long as I could with the Kindle, without getting eyestrain.
In fact, I actually find that I am getting less eyestrain with the iPad now,
because its backlit, and I dont need to be under a very bright light to have good page contrast, as I did with the Kindle.
If you need pocketability, and plan on reading outdoors though, you need a Kindle. I pretty much only have a chance to read books when I am at home, and prefer to do so in the evenings with some dim background light on the iPad.