I recently had to compare AWS and Azure for my company. I limited my comparison to AWS c3 and c4 class instances versus mid-range A and D class instances.
My tests are very limited I realise, but it looks to me like the AWS boxes represent better value for the money there, even in the on-demand range. Azure used to offer 6-month and 12-month plans but they removed those. Now you need an enterprise agreement to get anything other than published rates, and you need a big spend to qualify for that AFAICT. AWS reserved instances therefore make their instance rates even more competitive, if those make sense for you.
I sent all this to the company trying to push Azure to us hoping they would have better data to refute my simple benchmarks, but they didn't really have any coherent response beyond talking about the "other advantages" of Azure.
Beyond that I looked at the excellent data at https://cloudharmony.com/cloudscores (great site by the way). Their service is not live yet, so I scraped the data into Google Sheets and compared it there. AWS seems to beat Azure on most cases.
(Data entirely owned by Cloud Harmony). Sorry, I can't find a way to let viewers change the filter on the data.
As far as "other advantages go":-
* If you use Win Server 2012 + HyperV in house then there's a good reason to use Azure because of tight integration.
* If you're using SQL Server it's potentially a good fit too. (MySQL on Azure is recommended via a DB as a service they offer from a 3rd party which seems very pricey).
* If you're starting out and are using Visual Studio tooling then the tight integration with Azure Websites, Web Roles and Worker Roles would be pretty nice since the build/test/deploy process would be pretty slick. Re-engineering an existing system to fit the PaaS could be hard, depending on your architecture (it would be for us).
And with Win Server, I run ASP.NET and PHP and Node, it works nice. Db (pg) is on linux.