Load speed - simple as that - take a look at the two images from Google Chrome showing load times for various stuff with load times (not the same files, alas, but should give you the idea)
When we used the esri hosted API, there would be a 5-15 second delay while the client contacted Esri servers to check that the cached version it had was still valid. For local hosted this is less than 1 second
Also, there were times when the esri servers simply timed out, leaving our users unable to work.
Cheers
ACM