Up until a year ago, I'd have said paperback. However, after getting a Kindle Paperwhite I am now a convert to e-readers!
They're so light and easy to hold and it was great being able to bf my DD without disturbing her by turning pages etc.
One thing that put me off e-readers for a long time was that I often like to flick back through books to remind myself of who characters are etc. I didn't think it was possible on an e-reader, but on the Paperwhite it's actually easier as you just hold down on the name of the character and it brings up previous mentions of them to jog your memory. It's also easy to flick back to remind yourself of things that happened without losing your place. These might be features of newer kindles, however.
I've bought a waterproof case so I can read mine in the bath, though I spend ages putting it in every day which is a bit of a pain.
The light on the Paperwhite is great. I have bad eyesight and it makes it so much easier for me to read. The battery life is also great - it lasts for absolutely ages so I don't even need to take my charger with me anywhere (other than a two week holiday) as I know it'll last.
After being adamant that I preferred paperbacks and would never convert to e-readers I now find the prospect of reading a paperback quite unappealing. I had a shelf of books waiting to be read but I've given them away and re-bought on kindle. The paper didn't seem very nice compared to my kindle screen.
I have freed up so much space in the house by giving away my fiction books (I've kept the non fiction ones) and rebuying the ones I love on Kindle.
The children will carry on having proper books though, as I don't think electronic books are the same for children.