I have just bought an Amazon Fire TV box, and tried Netflix, YouTube and Amazon Prime movies. Despite claims in their advertising, the picture quality on the Fire TV box is poor, blurred and juddery. After a couple of days using it, I'm sending it back.
The picture quality of HD channels, Netflix and YouTube on my Virgin Media TiVo is excellent in comparison to the Amazon Fire TV box.
Although the Netflix and YouTube apps are sometimes slow on the TiVo, overall the quality of the Virgin Media Tivo is very good, and I will continue using it. Credit where its due.