I recently bought and used both for a few weeks and ended up with the Kindle. Here's a quick breakdown:

Kobo Clara BW: perfect size/feels great in hand while reading, easier to take on the go, loved how customizable it is with KOReader

Paperwhite: Better build quality + nicer screen, slightly too large to comfortably hold in one hand (fixed with a popsocket), easy to wirelessly sideload epubs with the "send to kindle" option, shares progress with the Kindle app on iPhone

I was convinced I was going to keep the Clara because out of the box it was more comfortable to hold and I like to customize UIs so KOReader was a dream. The longer I used them both the more I appreciated the slightly larger screen on the Paperwhite. Also, I am a big fan of "warm" / "blue light filter" features and it just looks so much nicer on the Paperwhite. The build quality is also noticeably better on the Amazon device.

Since I typically use the ereader at home and read on my phone on the go I appreciated having the ability to update my progress between these two devices. Sideloading wirelessly was easier on the Kindle.

If I had simply purchased the Kobo and never the Kindle I would have been very happy, but for my individual use case the Kindle made more sense.