Not only will the Apple iPad compete with the Amazon Kindle as an e-reader, but because Apple's new tablet will run iPhone apps, it will compete with Kindle's software, too. People who buy the iPad can choose to use Apple's new iBooks app and bookstore, or they could opt to run Kindle's iPhone app on the device instead.
The decision might just come to down to the book stores. The iPad's iBook store may be new, but the concept behind it is not; it's not all that different from Amazon's Kindle store for iPhone.
What's interesting is that the Amazon Kindle book store will work on the iPad from day one, albeit only in 2x mode (pixel doubling to fill the larger screen). However, as the SDK for the iPad is out today, Amazon has plenty of time to prepare its store for the larger screen of the iPad over the next 60 days.