Not much difference. You just earn more points and better reservation gurantee but you will also pay much higher rate for that benefit. Other benefits are all the same.
Unlike Starwood hotels or Hyatt, whom upgrade their top tier customers to a luxury suite, Hilton does not do that and the maximum upgrade you will get weather you are a gold or diamond member is to an executive room with an executive lounge access.
Last year I lost my Diamond status and i went down to GOLD and I didn't notice any changes in the way they treat me when I check in at any hilton