The only thing that could kill either of them at this point is Apple screwing up big time. Even then, they would be slow to die. Look at how many times Windows has endured through a major flop of a release.
My point is this: unless Amazon is really stupid (which they've shown they are anything but), then they probably are not attempting to release it or promote it as an iPad killer. It's other people that try to set it up that way. My assumption is that they are going after a section of the market that loves the idea of the Kindle, but wants more from it.
To your point, the Fire needs to be sufficiently different from the iPad. So different that consumers don't look at it and simply say "So...it's an iPad without native email?" Or some other rhetorical question to that effect. If people look at this device and think "iPad, but...", then the game's already lost.
The Fire (lousy name) strikes me as the first true media tablet. I don't think Apple views the iPad as just a media device though it has been classified as such by analysts.
The problem for the Fire may be competing against the Kindle. Many people use an iPad along with the Kindle because of the e-ink display. Would a customer spend extra money just so they can play music and video?
It doesn't seem to have been, but no few people were predicting that it would be.
When in doubt, I take what people who are paid to write about the tech industry say and assume the opposite.