As for choosing between AWS and Azure, you should be able to run your workloads in either. Price-wise, Microsoft recently committed to matching AWS pricing, so no difference there. For running Microsoft workloads, it's worth considering that Microsoft supports the whole stack all the way up for Azure workloads, whereas I'm not sure how much support Amazon is able to provide when strange things happen in IIS, for example.
Pricing for Azure: http://www.windowsazure.com/en-us/pricing/calculator/
That said, I think the first thing to decide would be whether you're looking for Infrastructure as a Service (IaaS) or Platform as a Service (PaaS). The Iaas approach means forklifting your current servers from where they are to the cloud datacenter, with little else changing. The PaaS approach means refactoring your website or application to run on top of Azure, for example, rather than within IIS on your server. This would probably mean more work but you would get all of the benefits of a modern web service built for the cloud. See for example:
You also mentioned SSDs. If that implies you have performance intensive requirements, make sure you set up some test servers and get a feel for the performance in AWS or Azure first. My testing in Azure has shown excellent read speeds, but not screaming write speeds. And you won't get SSD performance. But there is plenty of caching going on, so that may be OK. Capacity-wise, multiple TBs of data are no problem.