I am at the planning stage of a web application that will be hosted in Azure with ASP.NET for the web site and Silverlight within the site for a rich user experience. Should I u
One other consideration is latency. There used to be a site that Microsoft ran with microbenchmarks on throughput and latency of various object sizes with table store and SQL Azure. Since that site's no longer available, I'll just give you a rough approximation from what I recall. Table store tends to have much higher throughput than SQL Azure. SQL Azure tends to have lower latency (by as much as 1/5th).
It's already been mentioned that table store is easy to scale. However, SQL Azure can scale as well with Federations. Note that Federations (effectively sharding) adds a lot of complexity to your application. I'm also not sure how much Federations affects performance, but I imagine there's some overhead.
If business continuity is a priority, consider that with Azure Storage you get cheap geo-replication by default. With SQL Azure, you can accomplish something similar but with more effort with SQL Data Sync. Note that SQL Data Sync also incurs performance overhead since it requires triggers on all of your tables to watch for data changes.