If you have videos on or subscriptions to iTunes, Netflix, and Amazon Prime (as I do), there's no box I'm aware of that will let you watch all three. So you end up using your Apple TV and then Roku or another box -- the Playstation 3 in my living room takes a long time to boot, and a long time to load the Netflix app, draws quite a bit of power, and is overkill for merely watching streaming video. The Amazon Fire TV, assuming it's fast enough, will add another device to my living room cabinet but make it a lot faster to switch to watching Amazon Prime videos.
Ideally Apple would allow Amazon to add Prime Streaming to the Apple TV box, or Roku would get the iTunes library. Then I could have an all-in-one box. But we all know that's not going to happen...