So as someone who has been knee deep in Azure for around a year but who had previously used AWS for 2-3 years I would say: it depends. If you are looking at PaaS offerings, specifically around the application hosting side (not database) I would say Azure is an awesome fit. The idea of deployment slots in their Web Apps offering is really cool I think. I personally like the ARM templates for automation compared to something like AWS Cloud Formation. Of course if you are using a Microsoft stack the integration with Azure is going to be pretty tight. 3rd party products are bit hit or miss.

If you are looking to do all IaaS or some type of PaaS database outside of MSSQL I'd point you at AWS. I think all of the providers at the core level are probably pretty similar when it comes to IaaS VMs but AWS has a leg above when you look at the whole process. AWS has tons of tooling (both native and 3rd party) built around it, plus you can typically find answers for issues via Google, something I think that is less likely with Azure.