If you only deploy your database to SQL azure and leave your web app on your local server (or hosted elsewhere), then the application may be pretty slow depending on the network speed between the server where the web app lives to where the azure server is that the app connected to at the moment. Moving small amounts of data will be quicker and may even be cached (or could be CACHEd) in a dataset on your web server, reducing hits to the SQL azure server.

If you deploy your application to windows azure and your database to SQL azure, then you are likely to have better performance.

Jim