Google Play's e-book store.
Google Play and Kobo both let you read your purchases in a desktop browser, or else on mobile devices. Both offer iOS and Android apps, while Kobo adds Windows Phone 8.
Both stores also let you download e-pub files protected by Adobe Digital Rights Management, which you can copy to any e-book reader except an Amazon Kindle. While Apple and Amazon also sell e-books, you can't download e-pub copies to transfer to other devices.
Kobo's e-book store.
If you're downloading e-pub files then there's no real difference between the Google and Kobo stores. Throwing random authors and titles at them, the stores offer a similar range and it's best to compare prices book by book – new releases tend to cost the same but prices can vary on older books.
The differences become clearer when reading on mobile devices. Both apps provide a slick reading experience, but the Kobo offers the choice of more fonts and background colours along with an orientation lock and built-in brightness slider – making it easier to read at night. The Kobo also tracks stats and achievements, which may encourage young readers.
As for sharing accounts and books across devices, we installed both apps on a mix of 11 Android and iOS devices. Google let us open only six copies of the same book at once, while Kobo happily let us open the same book on all 11 devices simultaneously (your mileage may vary here). One benefit of the Google ecosystem is that you can upload your own e-pub and PDF books to your account and share them between your device, as long as the books aren't protected by DRM.
Kobo's slicker app and more generous book-sharing limit makes it the better option for busy households, unless you're particularly keen on the ability to upload unprotected e-pub and PDF files to a Google account.