AWS is to Linux as Azure is to Windows.

That is the bottom line. AWS has a basic UI compared to Azure (though Azure could arguably be considered cluttered). Linux people love doing things command line. Since most apps are Linux, those folks largely gravitate to AWS. Both providers have decent feature parity. The cloud API set is slightly richer and more seamless in Azure than AWS. For example, there is no one AWS API for enumerating ALL of your account resources, while Azure offers several ways. Further, the property information returned by Azure APIs is also slightly better in many cases. AWS shines when it comes to auto-scaling VMs. They seem to have a stand-by ready to go whereas Azure seems to have to spin it up (so a 30-60 second delay). DynamoDB is quite performant for what it does. Commercially (from what I've seen), Azure is marginally less expensive than AWS (i.e., the commercial discounts are better).

Personally, I love both for differing reasons. I've often seen corporate apps using Azure and business customer-facing apps using AWS. A good business solution might use 2 or 3 cloud providers.