Attila123,
I think you mean Airbus A340-300 for HKG-ROM sector as A330-300 does not have the range to complete the sector as a non-stop flight.
CX codes its aircrafts according to the product installed. For example, the code 34C refers to Airbus A340-300 aircraft installed with the new First and Business Class products.
On the other hand, 333 refers to Airbus A330-300 with three class configuration. Normally, Airbus A330-300 have two class configuration and is used mainly on the Asian sectors with Perth,Brisbane, Colombo, Karachi on its scheduled days.
"34S" refers to Airbus A340-300 with new First Class configuration.
As etravelconsult pointed out in this forum, CX has already installed nine aircrafts with the new Business Class product.