We use AWS for a large corporate client, currently migrating applications to AWS. Everything was within the company's data-center but it was becoming too costly to maintain and retain staff. We have had a few costly downtimes, which is always a panic and requires calling in staff to work through the night. With AWS, all of this is taken care of.
The huge advantage with AWS is the cost and simplicity to use. We are in the process of migrating our applications.