For streaming, I still prefer Netflix. I don't like the interface of Amazon on the firestick or the phone app, though I do like a lot of the options Prime has that Netflix lacks.
For me Netflix is unusable of mobile because I simply cannot stream on LTE. I have a 1GB/day cap which gets blown away in 20 minutes. Prime lets me download shows on wifi and watch later.
Not long ago, Netflix introduced the ability to download certain movies, too.
I can see the frustration on that. I don't use mobile for Prime or Netflix, always wifi. But, I use Amazon Prime Music, and it seems to be much better designed for mobile than other streaming services I've used.