I own and love both.
It all depends on how you want to consume your media.
If you like to send web articles, have lots of "personal document" books in your archive, and want an all around better web experience, go with the Paperwhite.
It has x (3?) years of UI improvements which make a big difference in my eyes.
And my DX doesn't get touched anytime after the sun goes down.
But the DX is great, perfect for sitting outside with a cigar on a summer day.
Free unlimited 3G, etc.
If it had wifi, and I could send my web articles to it without hooking it to a pc, would make it so much better.
I see no reason why not to own both
