Wow, this topic has become really interesting to follow.
I have seen different reasons explaining why a brand is leader on a given market.
I would like to point also the first-mover advantage (which was implied in a previous reply, I think).
I can't back up that why numbers but I really don't think that Amazon does well *everywhere*. Japan and France come to mind. When I was in Japan, all I could find was Sony, Sony and Sony eReaders. Since then Rakuten bought Kobo, so the choice is a little bit wider. Don't forget that there wasn't any Kindle for the Japanese market before this summer (less than 6 months ago)!
In France the market is tiny with not advertised devices and deterring price tags for the content
. I have to say that I have never bought a French eBook so far, because of the price. I'm sticking with Project Gutenberg and eBooks in other languages.
Regarding the device, I don't expect the same from something worth of, let's say, $50 and something worth of $150. However, I expect both of them to be of good quality and reliable. I was looking at the Kobo Mini again this morning and definitely, fiddling with the settings can improve the user experience greatly. From what I'm read here and there, I tend to think that on the hardware level, Kobos don't have to feel ashamed. On the software level, well... I don't really know. Some maker don't really update their firmware. It's much easier to release a new model, thus creating a need for it. Kobo seems to try and fix things (like the "read" option).