Google App Engine is a very tightly controlled, and very inflexible, system for deploying applications which use google's App Engine services, Datastore, task-queues and an array of other useful things.
App Engine provides a very restricted development environment, you can choose from three programming languages, Python, Java and Go. For each of these they provide a custom modified runtime/compiler for running/building your application. The trade-off for this is that App Engine is able to automatically scale the number of instances of your application running to meet user demand (if you are able to pay for it). The restricted environment is somewhat idiosyncratic and is designed for scalability of stateless servers with a large, also idiosyncratic, datastore with memcached caching for speed. Good for a wide range of web-service development preferably with lots of independent requests which touch separate pieces of data.
It may not sound like it from the description, but I really like App Engine. But, it is important to know what it is for, and what it is not for.
Give it a try :)
The biggest difference is that you don't have to do any server management. You toss your app to Google, and they handle all of the deployment, distribution to multiple machines, load balancing, etc. I'm assuming that's the case for AE+Go as well.