The premier tier of banking is always the most expensive ones...
For the cup of coffee you get if you happened to go into the branch, there are really nothing much else you can get... Deposit rates are not drastically better (ok, occasionally you get slightly better rates but its not consistent) and they cream you off with special offering of funds, etc.. where the charges are actually higher (especially Citigold).
Real private bank (USD 2~5m) arguably offers some better and more sophisticated products that if you are aggressive enough you can try catching. But I would also argue its not really that significantly better than retail bankings.
Just stick to the listed market for investments,