I've had a Fire TV box for a couple years now and love it. It was really cheap one Black Friday and I prefer the CAT-5 connection to wireless, so I went with the full version.
I just installed a current generation Fire Stick for my parents and it works well, too. Theirs is positioned next to the router and does not have any noticeable buffering lag.
Neither of them is jailbroken, so I can't really speak to that, and I am still a cable subscriber so I don't know how well it works as a flat out alternative.
Netflix loads much faster on the Fire than on my X1 router/tuner.
If you have a Prime membership, it's a no-brainer to pick one up, IMO.