I can't tell you how gratified I feel reading some of the comments on here. I've been an LCD/TFT/Transflective(!) e-reading advocate for years. I used to read mainly on a Palm TX and have had this argument so many times. For some reason some people reading off these backlit screens have the brightness turned up full with black text on a pure white background and then dismiss it as being hard on the eyes after ten minutes.Essentially they're staring at a bright white screen without blinking for that duration. Light gray text on a black background with the brightness dialled right down is my preferred way to read off the Palm, and I've used the same set-up on iPads, Android tablets and even cheap MP3 players.
This is nothing I discovered independently, but it was a factor on many web design and usability websites for years. Thankfully that message seems to have gotten out to the wider public - something I never seemed to manage in my own "discussions".
I have a Keyboard Kindle and a Kindle Paperwhite - I found the non-backlit keyboard Kindle to be a real effort to read off. No eye strain as such, but the contrast was so poor and the requirement for direct lighting meant I didn't use it all that much. The Paperwhite is fantastic though. A side-lit e-ink screen is pretty much perfect for me, with great contrast and visibility coupled with fantastic battery life. Honestly it's the battery life that has now killed the back-lit screens for my day to day reading, but in a pinch I'm perfectly happy to go back to them and if I could only have ONE device then a Kindle Fire HD, or similar Android tablet would be perfect, allowing me to not only read but play games and browse as well.
That's a whole other point. People will tell you that they can't, having browsed the Internet for hours on end staring at a LCD or LED screen, read off anything except an e-Ink screen. Arrant nonsense. It's like the loons who claim that mobile phone signals give them headaches.