There is no "best" streamer box: there's just the best one for your needs, whatever those needs may be. On the other hand, the worst one is the Amazon FIreTV: you get all the lockdown of iTunes without the need, since you can watch Amazon on other devices.
Basically, AppleTVs are only for iUsers with iTunes media. That part is easy. As mentioned, FireTV should be avoided. That leaves AndroidTV and Roku. Roku's a classic and simple, easy to use setup for streaming, but it's not ready for UltraHD yet, the next gen of devices might be but they haven't been released yet. So if you want 4K, go with the SHIELD box (so far it's the only AndroidTV with VUDU support). A nice bonus with the SHIELD is support for some Android games, which will generally be cross-compatible with your Android phone at no additional cost. But if you don't need the 4k support, or the Android gaming support, it's not worth the premium over a Roku3, which is a pretty sweet device for the price.
I tend not to include game consoles when comparing streaming boxes. If someone wants a game console, they're going to buy it and play games on it, and as a bonus they already have streaming capability. But I don't recommend buying them as streamer replacements.
I'm very interested in seeing Roku's new, revamped lineup thats dropping in a couple of months, it may be worth it to wait for those and see how things shake up. If they can put a 4k device at the $100 price point or less, and Xiaomi can get VUDU onto the MiBox, we could have a very interesting competition.