If you don't already own a streaming box, I would highly recommend the fireTV. It trounces the other streamers currently on the market without limiting the services on the device exclusively to Amazon. Netflix users can rejoice! Here's the kicker: Apple is no doubt way ahead of Amazon. It's only a matter of time before they introduce the next generation Apple TV. To be honest, the Adreno 320 graphics chip inside the fireTV is a bit dated, however, very powerful. Apple's custom 64-bit desktop class A7 chip is way more powerful and has been on the market since September 2013 and if Apple decides to introduce the next Apple TV with the A8 chip, it's game over fireTV in terms of performance.
Each device is set at $99 but it's really all down to functionality and what will work best for you. If you absolutely must buy a streaming box right now, the fireTV is a no-brainer. But I would recommend waiting, as the fireTV is sure to light the competition ablaze.