According to the source data used for the model A332 cruise fuel burn on cruise at FL370, midweight, is about 5600kg/hr, and for A333 about 4800 kg/hr. And 6300/5300 for a higher weight scenario.
A330-300 is lighter in terms of weight (MTOW), not the other way around like you said (looking at the baseline variants).
Checked the actual A330-300 flight manual, chapter Peformance-Cruise-Cruise Tables. Cruise at Mach 0.82, standard conditions, FL370, 200tn weight says the fuel flow is 2900kg/hr/engine -> total 5800kg/h. For a mid-weight scenario (160tn) the flow is 2473/engine -> 4946kg/h. Don't have the A330-200 manual here to check it's values, but these A333 ones are rather close to what the other source says (5300 vs 4800) - but the weight and level have a big effect here.