I don't know anything about Kobo, but Kindles are limited to one Kindle device per account, so you can't share an account across two Kindles, and you can't share books across two accounts. It's one of the only big frustrations I've found since both my wife and I got our Kindles. There isn't any restriction on the Kindle app running on other devices however, so you can access the same account through a Kindle and through the Kindle app on an Android tablet (for example), just not through two Kindles.
i7-6700K ~ Asus Z170I Pro Gaming ~ 16GB Corsair DDR4-2400 ~ Gigabyte Windforce 3X 7950 3GB
Noctua NHU9S ~ Corsair Obsidian 250D ~ Corsair RM650X ~ Crucial MX100 512GB
SMSL M3 ~ Sennheiser HD555 ~ Logitech G500S/G15/G25 ~ BenQ FP241W