Here, we pick up data from Google Play, which is the most visited website for Android phones. As we know, every Apps on there has reviews, so the chat showed:
So, from this chat, we can find out that Kindle is the most popular app. But we should do some much more, because iBooksReader is the most popular reader app on iOS platform. And now, we use the Google Search Trends, get the chat like that:
Now, we can be sure that Amazon Kindle is the most popular eBook reader app for smartphones. But why? I think the reason is obvious, Amazon is the biggest books sellers in world wide, its has the most resource of eBooks.