If you are looking at which service provider to go for then you are correct there are a number of options available.
Recently, I attended a talk with Scott Guthrie and he demonstrated the strengths of Azure. I happened to have a friend sat next to me who was developing his site using Amazons App Harbour services. He felt that based on the presentation by Scott Guthrie that the Azure offering was too good an offering to ignore. Apparently the pricing structure (according to Scott Guthrie) for Azure has attempted to match App Harbours, but the features that are available were enough for my friend to decide that the Azure offering was too good not to take advantage of.
Just so you know, my friend is developing an MVC website with a document database (I forget which) with the standard JQuery UI etc.
If you are planning a similar venture then I am sure both services will be sufficient, but after weighing up what is on offer it seems to be obvious that you have more features from Azure than App Harbour.
For a better description see this: Windows Azure or Amazon EC2 for ASP.NET MVC Development?
One thing to note is that there is about to be an update to Azure soon which from my experience will make for a better user experience.