This isn't surprising actually. The servers used in Windows Azure are currently mostly 1.6 GHz machines. The larger sized machine you use the more cores you get, but they are all the same speed. This likely is a much slower CPU than the development machine you use.
On Windows Azure Web Sites when you move to Shared mode you are still in a multi-tenant environment, so you could be seeing some noisy neighbors here. The difference between Free and Shared is that many of the quotas for free are removed since you are paying. When you move to Standard then you are assigned a Virtual Machine dedicated to your web sites (up to 100 of them), so that is the best case scenario since you are the only one using the resources at that point.
There was a thread on this on the MSDN forums a while back : http://social.msdn.microsoft.com/Forums/windowsazure/en-US/0d0a3a88-eac4-4b9e-8b10-4a547cbf653b/performance-of-azure-servers-slow-cpus?forum=windowsazuredevelopment
They have started offering different hardware configurations with more memory for Virtual Machines and Cloud Services and such, but I'm not sure the CPUs have been changed. It's hard to find the CPU stated on WindowsAzure.com anymore, but on the pricing calculator for Web Sites it references 1.6Ghz machines when you move the slider to Standard.