I've got no figures to back up this post but I did study physics as the subsidiary subject for my mathematics degree, so I'll throw in my own views (for what that they may, or may not be, worth).
A gas central heating system is powered by (hopefully) blue gas flames which then heat a boiler. That, in turn, distributes heat throughout the house. Blue gas flames (rather than yellow ones) provide the most heat from the available energy but there are significant heat losses as the water is pumped around the system to (eventually) heat the air in a room.
A gas fire heats the air in a room directly and should therefore (under ideal; conditions) be more efficient. (i.e,. there are no heat loses as water is pumped around a central heating system). However that assumes that the gas fire still has a blue flame. Some gas fires are deliberately designed to introduce more oxygen into the mixture which is burnt, in order to produce a yellow flame (which looks nicer to many people but adds to their fuel bills).
For reasons of economy I'd always prefer to have a gas room heater rather than gas central heating , but I'd definitely be hoping to see blue flames rather than yellow ones.
Chris