First, I think it might be the only device that has Netflix, Amazon Prime, HBO Go, YouTube, and Hulu all on the same device. Most of the others seem to be missing at least one of those (Apple TV missing Amazon Prime, FireTV missing HBO Go).
The apps on the Roku 3 seems to be far superior to the Apple TV and Fire TV and seem to be updated more frequently. So I find the Roku 3 much easier to use because the apps have much better UIs.
Roku 3 doesn't have as powerful hardware as the Fire TV. Yet I find my Roku 3 is just as fast as the Fire TV most of the time.
The only good thing I find about my Fire TV is it's good for playing some Android games on the TV. So it can be an Android gaming console in the living room. I was able to plugin my USB Xbox 360 controller and play games quite nicely (and this is where it's more powerful processor shows it muscle). But other than the first day, I haven't really played any games on my Fire TV, I have an Xbox 360 for gaming.
Also the Roku 3 has a ton of channels you can add, far far more than the Apple or Fire TV. Granted a lot of these channels don't have much content. Syfy channel for example seems to just play clips from shows. But there are a lot of other nice ones like Crunchyroll, Revision3, CollegeHumur, Vevo, Plex, Flixster, Cnet, IGN, TechCrunch, Watch ESPN, Asian Crush (Korean TV), Smithsonian Channel... that's just a few of the good ones I've added to my list.