Well, technically, both have some level of management which is bundled with the services. Ex: I don't have to literally put out fires if one breaks out in the server room.
App Engine's management service by contrast is very tightly bundled to the hosting services... so tightly in fact that the cost of the management service they provide is exactly proportional to the cost of the resources I consume. It's a great deal. But we are getting off into the weeds here.
App Engine simplifies server admin for me. I have never had to personally 'bounce' anything for any reason. I don't worry about running out of disk space. I don't have to worry about sweeping out the sessions (on disk or db). I don't have to setup database replication. I don't have to configure rolling archive tables to improve the speed of access to the most commonly accessed data on a large table.
