Even though Rackspace and Amazon provide similar tools and products they both are built on different principles and have a different agenda and mission.
As expected this is going to shape the company image, product and services offerings. As there are countless metrics and ways to compare I would like to take a look at the user experience and evaluate a easy of use only.
You can learn and experience this yourself when setting up a simple test infrastructural build of Apache Web Server, MySql Database and Tomcat Applicatin Server. Alternatively we can learn from other and these 2 blog posts representing a very interesting summary:
Amazon and Rackspace: A Comparison, Part 2
Amazon and Rackspace: A Comparison, Part 1
A short summary:
Rackspace cloud is easier to use when interacting with cloud for the first time. The emphasis is on simplicity rather then elasticity and richness of features.
Amazon is much more mature and feature full. Unfortunately this leads to a longer learning curve and requires more knowledge when building your own infrastructure.