If you use CloudFormation, you get auto-scaling. In fact, if you write your own CloudFormation template, you can get easy drop-down menus of minimum / maximum instances, and how many to scale at a time.
No, Amazon doesn't have direct publishing from Visual Studio, but we've worked around that by using a Jenkins continuous integration environment and Chef. Jenkins automatically builds any code merged into watched Git branches, and if the build succeeds, drops it into an S3 bucket. In 15 - n minutes, the dev / stage servers will run Chef, which sees the new version and deploys it per the app's recipe. It all happens as soon as someone code reviews and merges the branch back.
With RDS, you've got so many options for backup it's not even funny. You can have read replicas in different availability zones. You can have snapshots. You can use Cloud Protection Manager to automatically snapshot. You can use replication to pull data out of RDS to a database running on an EC2 instance for ETLs, or to ship it somewhere else. You can use that same replication to have it sit on an instance where you are running a database backup daemon of some type, which offloads that work from your production database. The only thing you don't get with RDS is access to the OS image it's running on, or the filesystem. Anything else is fair game.
As the other guy said, Azure holds your hand more, and is much more Microsoft-centric. But the offerings are not nearly as deep, or as wide. Especially in networking - with AWS I create multiple private clouds that are walled off from each other and geographically separated, and only allow the traffic that I want across a VPN tunnel for DR purposes. I can peer together AWS virtual private clouds to allow network access between the all the instances, but retain security for departments to only manage instances in their account, in a web form that takes two minutes to set up. Also, because of some luck, we're leasing space in a datacenter where Amazon has a DirectConnect node, so we can physically peer our company's network with a few VLAN tags, a fiber pair, and setting up some BGP neighbors; which also saves money on the network data because it's no longer going out through the Internet to get back to our datacenter.