I have both (and am sneaking in at the end of the month at the current $79 price for my renewal).
The Netflix streaming player is much more mature than the Amazon streaming player (Amazon's is basically a half-step up from YouTube).
Netflix will save my spot and I can get miniscreen previews as I'm selecting where I want to be in a film.
But Netflix can be tetchy at times. Trying to manually pick a time point in a film in short succession usually winds up leading to an endlessly pre-buffering scenario until I refresh the tab.
The shipping is nice though, for when I order things.
With Netflix, if they don't stream what I want, I have to waste time with shipping a DVD.
With Amazon, they have a decent amount of content available for free, and if I want more, I can purchase (or in some cases rent).