Just how secure is the data I put on SQL Azure?
Irrelevant. Seriously. It is irrelevant how secure it IS - if she is in a regulated industry, the provider has to provide the necessary guarantees, whether he fullfills them or not.

And you will find that Azure tells you nothing in the contracts. It is thus not good to use them, regardless how good their factual security is.

Example answer:

https://stackoverflow.com/questions/11167152/hosting-a-pci-compliant-app-on-azure

about azure PCI compliance - the asnwer is: not.

Check:

https://www.windowsazure.com/en-us/support/trust-center/compliance/

for more information. This is what you are guaranteed - the factual implementation is then not your problem.