Why I read on the iPad
I have iPad Pro 10.5 for a few years. I was always a type who prefers a "small" phone + tablet instead huge "phablet" device, popular among Android phones and recently iPhones as well.
Although I have Kindle for about 10 years (currently Paperwhite 4) and a small library of paper books, I spend the majority of time reading on the iPad.
The device I read depends on what I read
Type of content I consume matters for me a lot. Let's say that the form follows the content. Recently I rarely read belletristic books - when I read them, I often spend time on long, many hours sessions, often at night or before sleep. When I read them - I use Kindle. E-paper is good for many hours sessions and doesn't hurt my eyes or impact my sleep.
What I read are mostly articles, comics or "heavy" books related to IT, business, psychology etc.
Why not paper?
Maybe traditional books have their "magic", but from a pragmatic perspective, I try to get rid of them. They are expensive, require ecological cost, not practical, heavy and space consuming. They require a light source and when my eyes are tired and I can't increase the font size... The only thing I enjoy in paper books is scribbling with markers and note-taking, but there are not many books I return to often (but there are few - I keep them in paper form).
Why not Kindle?
Kindle is great (and probably other e-paper readers too), but I don't find it comfortable reading anything but prose. It can't handle PDFs which don't scale, it's grayscale so I can't read any texts where colour is important. It also doesn't synchronize well with my other devices and its responsiveness (touch screen) is far less comfortable than modern displays. That's why I use Kindle when I want to read a classic book for pleasure.
So the iPad is left
iPad is performing well for me for most of my use cases. I read articles in Feedly, Pocket or Google News every day - iPad's size is comfortable for me and allows me to quickly check, save, archive etc. the content. The iPhone is too small for this.
When I read the non-fiction book, I use iBooks, which synchronizes well between my Mac and iPhone. It can also sync highlights, notes or bookmarks. Sometimes I finish reading on the iPad to continue reading on iPhone in public transport. On Mac, I can drag'n'drop PDF file to iBooks and after few seconds I can read it from iCloud directly on any of my devices. Many of these documents are PDFs scaled or scanned in A4 format, which may be a little bigger than 10.5 screens, but it's very easy to quickly zoom in. And mentioned comic books - you can read only on iPad or computer (which hurts) if you don't want to buy very expensive and poorly available paper books.
Finally, I also read content from apps like Blinkist or Instaread, which is not available on Kindle or paper.
Doesn't iPad hurt my eyes?
This is the core argument against LED display - they shine and hurt eyes. And this is technically true if I read for a very long time. But - I don't. For many hours sessions, I use Kindle and for hard non-fiction books, I spend maybe 30 minutes a day because my brain is getting tired before my eyes. Articles are short anyway. This type of content just require me to read it very slowly, so I don't mind that I could have read it faster on Kindle. Finally, the iPad has a built-in night mode which works very well and I don't recognize any special problems with sleep or focus.
To summarize, I use the iPad as a very handy multimedia device, so I can use it to do almost everything, including reading. Even if Kindle can do the same things better (let's imagine big, colourful and responsive screen), I will still prefer the iPad because it's all in one device.