CitiGold gives you access to a Personal Banker and a whole set of different staff, resulting in a world of difference in the customer service experience.
The difference is minimal because the Citigold banker can't touch your investment. Their jobs are no difference from typical Citibank bankers.
My experience with Citi call centers has been horrible and my personal banker eliminates the need to deal with that, making a world of difference.
Citibank scores the bottom in term of bank satisfaction among 4 major banks in the U.S. per J.D. Power. Surprising - Chase is the best, while both BofA and WF come very close (with BofA slightly better than WF).
You also get access to the CitiGold branches - which in some countries is a huge difference again with regards to experience.
Access to Citigold depends on if the local branches have access to your accounts.
In many cases, a local branch has access to a local Citigold account only.