The iBooks app is better. But Amazon Kindle Store is cheaper and has a superior selection.
Publishers are responsible for creating and making available the books in each store. Sometimes a book is exclusive to one store. In that case, you have no option of where you purchase it.
When a book is available in both stores, you must compare the price and quality on a book-by-book basis. This is easy to do because both stores offer free sample chapters. Books tend to be better formatted in the iBooks Store than in Kindle's Store. This can be critical for some genres, such as technical/programming books with graphics, code samples, and tables.
iBookstore purchases can only be read on iPhone/iPod touch/iPad/Mac. Kindle purchases can also be read on Amazon's dedicated Kindle devices, Microsoft Windows, iOS, BlackBerry, Mac OS X, Android, webOS, Windows Phone, as well as in a web browser.
- better interface (you even can turn off the skeuomorphic design features, if you prefer)
- it has less features, but the features it does have are better: dictionary, highlighting, type/fonts, footnotes, navigation, look and feel
- better PDF support
- iBookstore built-into-the-app for convenient browsing and purchasing
- Sharing feature where you can publicly publish snippets from your book to kindle.amazon.com for linking-to in Twitter/Facebook. Example.
- Amazon creates an email address for you to send documents to your Kindle via email. E.g. firstname.lastname@example.org
- Con: You have to jump out to the web browser to browse and purchase content.
On an iPad, I prefer reading in iBooks because Apple executes the fundamentals better. Amazon's Kindle app has some nice differentiating features, though. All that said, at the end of the day, nothing's better than reading a basic novel on a standalone e-ink Kindle device.