After a tour through the examples, it's safe to say that App Engine is not a direct competitor to Amazon's general purpose cloud offerings, such as EC2 and S3. App Engine is targeted directly at request/response web applications. Amazon's offerings are much more generic, allowing you to run whatever you want on EC2.
App Engine's data store is closer to a traditional database than Amazon's SimpleDB. With App Engine, you have a query language that looks and smells familiar. SimpleDB is a distributed hash. Both technologies are useful, but if you're comfortable with SQL, you'll find App Engine's Datastore more friendly.
Also interesting is that App Engine has direct support for Google Accounts. Don't want to write Yet Another Account System? With just a few lines of code, you have deep support for Google Accounts. Note that nothing prevents you from writing your own account management features. Too bad App Engine didn't have direct support for OpenID.
What's kind of cool is that you can lock down your application to users of a particular Google Apps domain. This might be useful if you wish to write an application for your company or organization. Nice touch.
When you register an application with App Engine, you have the option of binding your own top level domain (eg example.com). You do this through Google Apps. If you don't have your domain yet, it's trivial to purchase the domain name through Google Apps (via GoDaddy). This is very handy because all the work is done for you behind the scenes. I registered and new domain name, bound it to Google Apps, and then to my App Engine application within 10 minutes.
Time to downloading the SDK to full domain registration and application upload to running application: 1 hour. That was amazing. Of course, it doesn't do anything yet. But that's pretty cool.