What's the difference between Uri.ToString() and Uri.AbsoluteUri?

As a comment to an Azure question just now, @smarx noted

I think it's generally better to do blob.Uri.AbsoluteUri than blob.Uri.ToString().

Is there a reason for this? The documentation for Uri.AbsoluteUri notes that it "Gets the absolute URI", Uri.ToString() "Gets a canonical string representation for the specified instance."