I do have a Kobo, but it usually isn't worth the trouble to move my books over from my phone. It's only full sun that's really problematic on a phone, and that's hard on the eyes no matter what you use. A phone works fine in the shade. e-paper might work better there, but not enough better to be worth the hassle, since the vast majority of my reading is inside where AMOLED is superior.

I use my iPad most times too (indoor). But outside, I switch to my Kindle as e-paper display can be read everywhere and there are no annoying reflections. Also at least Kindle lets you sync your books, so you can continue reading at the same position on a different device (app) later.

With Kindle, you just open the book on your phone (after you spend 2 minutes setting up the app).