Both the Kindle and Kobo are using an XGA panel. So the DPI/resolution is the same. I don't know who is correct or not about the DPI, but it is the same for both readers. Kobo might be using the plastic backed panel from LG. No idea what Amazon is using.
One big advantage the Kobo has over the Kindle is that the Kobo handle ePub while the Kindle does not. Also, we don't know if Amazon has fixed the display issues with KF8 in the new Kindle's firmware.