The Amazon Video on my Galaxy S5 only downloads in SD, even for movies that I have purchased in HD. Since the screen is small, I'm not sure if it makes that much difference although you can barely see some blur in very fine detail at close viewing distance. At least they're honest about it and don't pretend it's real HD.

My Kindle Fire HD 8.9 downloads HD up to 1080. That isn't a new feature, it's been available for a couple of years. With the bigger screen the HD does make a noticeable difference in video quality. So the Kindle is a better option for video rather than a phone.

The HD file size that I get runs about 1 GB per hour, which is highly compressed but it seems to work well and looks fine to me.