I'm trying to find something for my Mom. Something like AppleTV just seems way too pricey and while I know little about the 2 products I've listed, they seem to have good reviews and aren't super expensive. She's terrible with all tech, and I want to find something that shouldn't be too hard for her to get the handle of with a little coaching from myself lol. I suppose the main thing for her would be a user interface that is very easy to navigate.
My two cents: Roku wins this one. The interface is cleaner, there are less unpleasant surprises (e.g. clicking on stuff on Fire TV and finding it's going to cost you $13 to watch it), and the remote is more user friendly, with little quick launch buttons for Netflix, Hulu, etc. (I'm pretty sure you can install apps remotely on her Roku through the web interface as long as you have her password, as well, but I may just be thinking of the initial setup we went through with my daughter's Roku TV.)