NPR reported recently on a study that shows people who read on iPads before bed sleep less and get lower quality sleep.
One More Reason To Reach For A Paper Book Before Bed
Basically, the article talks about how exposure to certain lights before bed -- i.e., the blue light in the TV -- disrupt sleep and make it harder to fall asleep and get high-quality sleep. The article is clearly anti-ebook, and it's not until you get to the end that it gives a reluctant nod to e-readers that don't emit light.
Personally, though, I've never had a problem with my e-readers affecting my sleep, and I've used both kinds. I also have never had an issue with eye strain from being on either the computer or an e-reader for long periods of time, and I have a very strong theory about why this is.
I think the biggest reasons is because I keep all of my screens (laptop, tablet, e-reader, phone) only as bright as they have to be in order to see them. Since I am usually using them indoors, it means keeping them on one of the lowest brightness settings, and turning them up if I'm somewhere bright, such as a coffee shop with a lot of windows or an outdoor patio. (My phone is set to adjust the brightness to wherever I'm at, but with a max setting of about half brightness.)
I started out doing this because it preserved battery life, and for me that was most important, especially on my laptop. But when I accidentally left the screen too bright a few times, I found I quickly developed eye fatigue, whereas if I turned the screen back down I experienced none at all.
And since I've never had any problem with reading on a tablet before bed, I suspect that keeping the screen dim is helping there, too. I generally fall asleep almost right away after I turn out the lights, no matter how long I've read. In fact, I've found that I sleep better if I read for some amount of time before bed (probably because I'm so used to that routine, as I've done that for most of my adult life).
In any case, I don't think something like this should keep you from reading before bed, or scare you away from e-readers entirely. If you have problems with insomnia, just turn your screen brightness down, or get a black-and-white e-reader instead, and you shouldn't have any problems with it.