Cloudformation is piss poor compared to Resource Groups in Azure. The idea is similar but you can deploy 'stacks' of things with permissions for role based access as well, very easy administration.
As for the Lambda stuff -- that's WebJobs in Azure, and far more powerful (takes in .exe, .sh, .bat. cmd, etc) whereas Lambda does .zip and .js only. Beanstalk integration into .NET environments (which is what we are primarily) is very bad compared to WebApps, and MapReduce is pretty commonly usable on either cloud. If you use SQL the SQL Azure is a better offering than RDS, but if you're on PostGres/MySQL then definitely a point in the RDS favor. Dynamo is also available on Azure in another form, as well as API aggregation, mobile integration, etc.
Long story short is that I don't think that one is better than the other outright -- it's about choosing the tools that make sense for your environment and developers. For us that seems to be Azure given a heavy SQL/.NET platform and developer base. For others it may be AWS for other reasons. I just think that as Azure expands its capabilities, and some of the things they wind up doing a lot better than AWS, as well as the stuff they do that AWS can't do at all (ie micro services architecture support in Service Fabric, Machine Learning that is far beyond AWS' capabilities, etc), then AWS gets into a race to the bottom. Not to mention the segregated storage in AWS that they are working on consolidating (ie, the S3/Glacier/EBS/etc) whereas in Azure it's one storage platform that can be called by API for different purposes (like block store, drives, etc).
Right now Amazon's primary problem is the talent keeps leaving, and they don't pay enough, nor do they have the perks to keep people motivated to stay. They take existing open source projects and expand upon them and provide you a managed service primarily on the IaaS side, but nothing is really developed net new; it's all a rehash of things already made. And that's where MS is making strides... all of their software is a reimagining of what cloud should be, rather than taking their existing products and making them "cloud ready". In time I think MS will do very well, but the poor marketing as well as MS' poor image from years and years doesn't help them. That said... AWS can only stay in people's good graces so long until they just can't keep up the level of innovation that not only MS, but Google are doing in the Cloud space. And truth be told... if MS has to worry about anybody in Cloud, it's not Amazon -- it's Google.