I have Netflix and can watch some Amazon videos since I have Prime. I use Netflix more, even though I think it sucks (or at least their streaming service does). I am tired of Netflix taking shows off that I like and adding their own shows, and it kind of feels like that's the direction they're moving towards (i.e. more originals, fewer...what to call it...mainstream shows/movies?).
Amazon Video doesn't even make sense to me. Like, it seems like you have to pay for entire seasons or, like, $2/a video or more to watch their videos, unless you get Prime. And then with Prime, you can't watch everything, and I definitely can't watch anything I actually want to watch without paying more than what I pay for Prime (which, makes it at least as bad as Netflix is, but, really, worse, even though you do get to choose from a wider selection--but it looks like you have to pay per for some of it). If this is not the case, then I'm having a hard time getting clarity about that.
I am more into TV shows than movies, and it looks like what I'm saying applies way more to TV shows, just taking a quick look, i.e. there are a lot of movies you can stream without paying more if you have Prime. I also use Chromecast, and I can't use that with the Amazon apps whereas I can with Netflix...but I can if I stream from my ultrabook or laptop Chrome browser. At least with Prime, you get more than just access to videos. Netflix video quality tends to be better when streaming from my phone than from anywhere else.
Ultimately, I feel like Netflix vs Prime, Netflix is more a waste of money but mainly because Amazon Prime gives you access to other stuff (free 2-day shipping, Amazon Music, some Kindle books, etc). I would choose Netflix over paying $2 or $25 for TV series and whatever for movies on Amazon Video. They both kind of suck, to me, though, in terms of videos, but it depends on what you like to watch.