Obviously made by different companies, Kindle - Amazon, Kobo - Rakuten (A Japanese multinational).
When I was doing my research on what to buy, I was weighing up between the Kindle Paperwhite vs Kobo Clara 2e.
I think most people say that the Kindle has a better selection of books available in their store (though I’ve only had one book I couldn’t find for the Kobo, but I solved that issue by purchasing it while in a different region), and the Kindle is Larger. The Kindle also has a top screen layer than makes it flush with the body.
In the end I went into a physical store to have a look at both of them, and went with the kobo, mainly due to how I preferred the smaller size.
edit - oh and just remembered as I read another comment in this thread, Kobo is compatible with Libby, which is what is used to “borrow” ebooks from your local library (I believe in most places around the world?, not too sure on that), while Kindle is not. Though I havent used it yet, as when I went looking for a few books I wanted to read, they had already been checked out by other users, and there was a waiting list for them.