I had a Kindle PaperWhite a couple of years ago. After that, I was on Kobo. Every time a new device with a bigger screen came out, I got one, H20, Aura One... I recently got a Kindle PaperWhite 3. Partly because I finally wanted a smaller device. But I'm now back on Kobo, with the Clara HD, mostly because of the Kobo software.
The Kindle software has improved a lot since I first had one.
Things I like/miss about the Kindle :
- You can copy any fonts and adjust the weight.
- The smaller header/footer.
- The mini clock on top.
- You open a book and you have no ghost of the cover.
Things I like/prefer about the Kobo :
- Being able to manage my collections, by tags, from Calibre.
- Exporting ePub to KePub on the fly.
- Comfort light.
- Detailed reading stats.
I know there are patches that you can add some of the Kindle features I mentioned to Kobo. But I don't care enough about them to hack into my ereader. They're not always bullet proof, like the full page mode. When I saw that in the latest firmware that you can finally show/hide header or footer, that convince me to get a Clara HD. More text on a page and Kobo proof.

One thing I would like to see on Kobo, and I don't know how Amazon does it, is to open a book without any ghosting. I often have to flip a few pages in order to refresh the page before starting to read. Not a deal breaker, but really annoying.
I had a Aura One and I'm now happier with a Clara HD. Why? Size. It fits well in one hand. And weight. Way lighter than the PaperWhite, and smaller.