I have both (Sony BR w/ Apps + a Roku). The Bluray is convenient because you get disc playback AND apps, plus Youtube (the Roku doesn't have Youtube). However, the Roku has a nicer GUI. The Roku has a simple remote and an easy-to-use interface. The Bluray system has five million buttons on the remote and a more difficult interface, but you get Bluray playback and the Youtube app. Both cost about the same (~$99 depending on the model you go with).
If it's mostly Amazon and Netflix, I'd go with the Roku. Have my whole family on them. Super easy to use!